I've never found a mulching mower that could grind up the clippings small enough so they would disintegrate by the next week. We mowed hundreds of acres per week, too. And all our clippings had to be dumped in the proper 'clean green' dump that was licensed to handle grass clippings. Do you happen to have curb side garbage service? Ask for the landscape debris bin?
My own home back in the day I mowed 4 acres. "Mr. Toad's Wild Ride"! There are two ways to handle emptying the bag of clippings to save you from hoofing it to dump them; tarps or bins. Lay your tarp in the place you plan having a full bag. It is easier than it sounds. Have a couple of tarps, 10X12. You'll soon get used to being able to hit that tarp every full bag. Tarps were life savers. Of course it is nice to be the boss of some strapping men, too! The bins could be laid on their side, shove the bag inside, flip the bin upright, bounce it a bit to pack the clippings at the bottom and lay it back on its side again for the next dumping of the full bag.
Mowing once per week shouldn't be creating that big of a pile. Ugh. Stinky. Anaerobic decomposition. You could also start a fire, seriously as that depth of clippings creates lots of heat. Leaving clippings on the lawn is asking for major thatch problems and thatching actually means building a new lawn all over again. Not at all a fun project, and talk about debris!
I am assuming you have cool season grasses to be generating that much in clippings. How short are you mowing? Cool Season grasses need a minimum of 3 inch top growth left after mowing every single week. 3 1/2 inches would be better if you are able to raise your deck that high. I had my decks 'custom' raised. These grasses have huge root systems that need that much top growth to feed those roots. Fertilizer is not food. Plants make their own food and if there isn't enough blade on those grasses they will be slowly dying of starvation, allowing weeds to easily get established.
How do you water? Let us know what your maintenance habits are, what you use for fertilizer, how often you aerate that kind of thing. I think we can save you lots of work and have less clippings to 'drag' on your tarp to the curb side bin or your plant beds to dump thinly on the back side of the beds to smother weeds. no more than an inch or two thick. Any thicker and you cut the air from the system and you get anaerobic decomposition, stinky, slimy mess.
By cutting to the proper height every week you should be just grazing the top of the blades. Once these grasses get to 3 or 3 1/2 inches the growth slows down. This height provides your grasses enough photosynthesis to be vigorous, dark green and at this height the ground is shaded out not allowing weed seeds to germinate. Do not water every day. Water only when you walk on your lawn and your footprints stay down. Then water very deeply. Do not water again until you see your footprints.
This is how you train the roots of your grasses to grow deeper and make your lawn drought tolerant. By allowing the soil to dry out you also inhibit any weeds with shallow root systems. You'll have lush green grass when others have brown. Check out Dr. Earth's Lawn Fertilizer. Costs more but worth every penny and you will only need to fertilize 2 or 3 times not 4. Comes with thatch eating bacteria, too. Works more slowly than the synthetic fertilizers which won't stress your grasses and lasts longer. Aerate by pulling plugs and those you leave where they fall once per year. Sharpen your blades every other mow. Where is it that you live, anyway? Got lots of experience with this monster called a lawn to keep your investment and you as well, beautiful and healthy and happy.
The height and sharpened blades sounds great. I'd like a picture of your grass? Using tines to aerate? So are you sort of thatching? Interesting. Aeration HAS to be done only by pulling plugs of soil out of the lawn bed and letting them lie where they fall. Easy chore, really. Get together with a neighbor or two to share the rental; around $75 bucks. It goes very quickly but I make numerous passes while I have the machine.
They used to do wear spike shoes to 'aerate' using longish spikes. This only compacts the soil as the soil is squeezed tighter together. Plugs have to be pulled out of the soil (1/2 to 3/4 inch diameter plugs or better about 2 to 4 inches long). The organic debris decomposes and the soil is top dressed back into the 'thatch' zone with more thatch decomposing bacteria to do the job. Screws and moles do such a wonderful job without asking for a salary. Top dress, eat harmful grubs and aerate and there is usually only 2, a mom and pop operation. Babies are forced out to find their own lawns.
Every now and then don't be afraid to leave the clippings as long as you mowed the week before. I am amazed at this pile of decomposing grass clippings you've got. Make sure you mow every dang week (if not twice to be more OCD about the lawn). (I got very OCD about my lawns in my care). Need a pH test before any liming. Is the NE as wet as the NW? I've heard from friends in the NE that the rain has been phenomenal this year.
Use that footprint to determine when to water manually. Train those roots. I just read your comment that you are walking UP the compost pile? If you could send a picture of that we would really like to see what you are dealing with. We could help with the decomposition process. If it is still green, slimy, hot it is not decomposed. If you are able to see blades of grass in the pile, it is not decomposed. I'd find some high nitrogen fertilizer to throw on the heaps every time you dump your grasses; from a tarp or a big bin. That will hurry up the decomposition.
Since you have to worry about water restrictions lets work on training the roots to grow deeper. Sounds like you've got a great height left to feed those roots. The easiest way to do this is to watch your footprints. If they spring back up do not water. If they stay down then water and water deeply. Take a shovel and slice a layer 8" deep. You want to see moisture at least 4" deep if not 6". Then wait until your footprints stay down and water as deeply as before. Soon, you will be watering once per week even in the hottest part of the season. One inch per week is all that is necessary for trained grass crops. All your neighbors and the entire development should be doing this training of grass roots, plant roots. You might not have restrictions anymore. The neighbors that get out and water a little everyday are the ones wasting water. Allowing grass to go dormant is not at all healthy for a lawn!
Note: Just saw your pictures! Arghhh! Those implements/attachments are worthless for aeration. You have to have one that pulls plugs of soil from the lawn's bed. Those attachments are never beneficial to a lawn.
What kind of a 'mower' are you using? A riding mower where you can lift the deck up to a mowing height of 3.5 inches? You are mowing way way too short. That is a big deal. Without top growth that grass will never be vigorous and be able to make enough food for those grasses.
I also think you water too often and then not enough. Please look up other questions about cool season lawn care and maintenance on OUR site. I am assuming that this is the result of allowing your lawn to go dormant? Lawns are huge investments, I know this because I charged big bucks to care for these lawns...after these people had us install lawns and irrigation and care for these monsters for decades. Big investment. Makes me mad that the municipalities assume we can allow our lawns to go dormant with no backlash. We need to help you train your grass crop to never have to go dormant.
Your lawn needs all the help it can get so allowing clippings once in a while to stay on your lawn is OUT. Aeration, is IN. Let's talk about watering, okay? Who put your controllers on a schedule? Tell us more...any little thing you might not think that is important, just spill. This lawn is not the lawn of your dreams. You work too hard for a lawn this...sad.
Note: I am running out of comment space. True Green ain't my favorite company, no siree! They might have used a grub control that this next season will cause your lawn to become completely decimated by 'grubs'...crane fly? This company relies on customers with no knowledge of their landscapes and lawns. They set you up for failure, on purpose, I can't say.
Please find out what it was they used on your lawn. Perhaps we can ameliorate what they've used somehow. Seriously, these pesticide companies run on customers who do not understand the biology and botany outside of their homes and it makes me very mad. Pesticides are rarely if ever necessary! Pesticides cause more problems than they solve and those problems are only apparent the next year when the owners think it must be their fault so they hire these idiots again. Sorry.
I did total maintenance on my sites. To include fertilizer. One of my clients got talked into using another company for fertilizer after I had already and continuously applied correct fertilizer to this site.
I posted signs saying that landscape had been fertilized with what and how much. One week later I arrived at the site to find fried FRIED plants. This company, True Green, had fertilized again even though the signs said everything. Fried that client's plants, lawn, established plants and all. So sad.
We got a new contract to redo the entire landscape mitigating the chemistry, ripping out the dead and leaching and adding more soil to the beds, redoing the entire lawn as well. Broke my heart, great for my company I guess but what a waste!
How about another picture showing more of your lawn, the edges, the expanse? I spent a ton of my adult life getting to know maintenance and plants and that dang lawn. All the education one could hope to learn. On cool season grasses. Warm season is another monster crop I am only learning about. Wish I could live where there were warm season grasses, sigh!