i just use a wood sink i built and coated with rust-o-leum... i put a 2x4 on one side and drain it into a bucket (this has a pond pump-which drains into the laundry drain which was to high, for gravity to do its thing)... anyway... i thought of doing your idea, but the plastic bins i saw were not wide enough, and i didn't think of solution... my concern is that, the seams will spring a leak... even with silicone...
maybe if you use pvc glue and silicone (as a precaution) i think it will work... definitely with the pvc glue, that thing is incredible.
Are you sure a wooden sink won't work... that you could just stand on it's side (longways) and just take up minimal amounts of space. the benefits of this, is that you get to make it the perfect size.
what size are the trays?