Your wrote at the end of your question the following
Note: please don't get caught up in the details of if I should be
sending down 30,000 pieces of data or not -- this is not my choice and
there is nothing I can do about it (and I also can't change Guids to
ints or longs in the DB).
I think it's your main problem. If you don't solve the main problem you will be able to reduce the size of transferred data to 10 times for example, but you still don't solve the main problem. Let us we think about the question: Why so many data should be sent to the client (to the web browser)?
The data on the client side are needed to display some information to the user. The monitor is not so large to show 30,000 total on one page. No user are able to grasp so much information. So I am sure that you display only small part of the information. In the case you should send only the small part of information which you display.
You don't describe how the guids will be used on the client side. If you need the information during row editing for example. You can transfer the data only when the user start editing. In the case you need transfer the data only for one association.
If you need display the guids directly, then you can't display all the information at once. So you can send the information for one page only. If the user start to scroll or start "next page" button you can send the next portion of data. In the way you can really dramatically reduce the size of transferred data.
If you do have no possibility to redesign the part of application you can implement your original suggestion: by replacing of GUID "{7EDBB957-5255-4b83-A4C4-0DF664905735}"
or "7EDBB95752554b83A4C40DF664905735"
to the number like 123
you reduce the size of GUID from 34 characters to 3. If you will send additionally array of "guid mapping" elements like
123:"7EDBB95752554b83A4C40DF664905735",
you can reduce the original size of data 30000*34 = 1020000 (1 MB) to 300*39 + 30000*3 = 11700+90000 = 101700 (100 KB). So you can reduce the size of data in 10 times. The usage of compression of dynamic data on the web server can reduce the size of data additionally.
In any way you should examine why your page is so slowly. If the program works in LAN, then the transferring of even 1MB of data can be quick enough. Probably the page is slowly during placing of the data on the web page. I mean the following. If you modify some element on the page the position of all existing elements have to be recalculated. If you would be work with disconnected DOM objects first and then place the whole portion of data on the page you can improve the performance dramatically. You don't posted in the question which technology you use in you web application so I don't include any examples. If you use jQuery for example I could give some example which clear more what I mean.