As I mentioned earlier, a tray raised on a platform with a drain is very workable; You can even use an Ikea "Dilling" storage box (30 x 27 x 8" deep) as a tray.
Take a look at a standard bathroom sink - the chrome ring of the drain passes through a hole in the sink; the outside of the drain pipe is threaded, and a large collar-type ring screws upwards, against a rubber washer and fastens the drain to the sink. A "stopper" style drain "without overflow" (which uses a rubber plug & chain) is about 9 bucks.
You cut a hole in the tray with a hole saw; put a ring of plumber's putty or silicone around the top, pass the drain through, and use the rubber washer and the collar to snug it up against the bottom. This works very well, and the rubber squeezing it all together seems to keep it from cracking.
For washing, you can set the whole thing across a bathtub; stick a suitable piece of PVC in the tray-drain, which raises the drain a couple inches; pipe in some water (use one of those rubber wash hoses that sticks into a faucet from a photo supplier) - the water will fill to the top of the PVC and drain over (and into the bathtub) and function as a wash sink.
Heck, just using the bathtub as a wash sink is something I did back in the day.