How to develop large dark room prints?

No need for all that, you lay the un-developed print on a plastic drop cloth. Have the developer, stop and fixer in a plastic pail. Using a large brush, such as wallpaper's use to apply wall paste. Soak the brush in the developer, apply to the print. You can also use a paint roller. This is all done under safelight. Next stop with stop bath or use plain water. Follow with the fixer. Wash outside using a garden hose.

Nothing to it! Nobody said this stuff was easy. Don't forget to make small test prints if you what to keep the waste down by avoiding re-makes.

Soft kitchen sponges and plastic gloves (the kind you use for dishwashing). Expect longer times than when submerging.

It appears that you have the counter space but not the sink space, to put three large trays side by side.

Think outside the sink.

You do not necessarily need a sink large enough for all the trays, you could bridge the sink with a board or boards and place your trays on them. Paint the board with an epoxy floor paint. The board could have a cut out for the sink so when it is time to pour the chem's out to the trays you do it over/in the sink without having to do a lot of full tray juggling.

If you wanted to Get your DIY on, you could make a waterproof board or trough or sink, that way you can spill then wipe it all to the hole over the sink.

Perhaps it is time to get/build a proper wet side darkroom sink. I built a ten foot long sink with 10 inch high sides out of 10 foot long piece of cabinet grade plywood, i then had it sprayed with truck bed liner, I had them smooth down the liner before it cured so there is no texture. Waterproof, chemical proof and possibly bomb proof. (i know its earthquake proof, at least 7.2 magnitude - I can be hired.)

I am confident given the space you have to work with that you can make it work.