I had overseeded and dormant seeded for many years before I finally bit the bullet, killed my own lawn and reseeded with new seed. It was well worth the effort. Overseeding isn't a one year deal. It will usually take more than 3 years for the new seed to significantly overtake the old seed.
Without sufficient irrigation the weed seeds will dry out and your germination rate will drop.
If you want to try and recreate the conditions of dormant seeding keep the seed in a freezer in an airtight container, cut your lawn very short, apply your seed, roll it with a lawn roller, cover with a 1/4" layer of compost and roll again. I haven't tried this exact technique but I did something similar once involving freezing the seed and then let it sit in a can with moist used coffee grounds so it can start the germination process. I used this to patch a damaged section.
No idea how much rain you get and even meteorologists have trouble predicting... all I can say is try and plan to water as frequently as you can. At least two times a day is recommended. The compost will help keep the seed moist but will eventually dry out.
I don't have a sprinkler system but I picked up some components including a sprinkler timer that attaches to the outdoor hose bib (link to my site with opinions on products I bought and looked into) that I used when overseeding. They work well, are cheap and you can remove them when you're done. Your water flow and pressure will determine how many heads can run at once. There are timers that have multiple zones to be able to operate multiple heads.
You said it's your home and not an investment property so it shouldn't be too hard to water it. There are all sorts of hose end sprinklers you can use. I started out with impact sprinklers but they were too noisy. I figured out I could replace the spike base impact sprinklers with rotor sprinklers that are quieter (link to my instructions and video) and provide similar precipitation. I run my sprinklers early in the morning and didn't want to annoy the neighbors.
If you're killing the lawn you can also add a covering of straw to help retain moisture.
Clover in the lawn usually indicates low nitrogen. Send a sample of your soil to your local university cooperative extension office to check pH and fertility, doing an organic matter test would be good too. It's a small fee but will help you improve your soil which will take care of a lot of problems. The test results should tell you exactly what you need to do in terms of dealing with the pH and fertilizing.