I am currently developing a technology to transform random maps into completely symmetrical ones. I haven't been able to fully automate this process yet; I still have to manually adjust some settings. It takes about 2-3 minutes per map, but that's still progress. With a small change to the algorithm, it's possible to generate symmetrical 2x2 random maps as well.
If you plan to play something like this, let me know, and I can generate a dozen or so layouts.
The other day, I decided to test a 2v2 game with friends on a random map. It took a long time and was quite problematic, so for convenience and to reduce complaints, I suggest reducing the number of rests to one per team.