It is rectangular shaped like a bit more squarish brief case, has a clear plastic cover and the back and compartments are black plastic. 

It is an industrial building used by a plastic factory in LA, CA.

I have seen the trays that go in the bottom of a sink base, but I am concerned that water could leak down the sides of the sink base, ending up under the plastic tray, where it would not be able to dry and end up causing a bigger problem than if there was no tray in there in the first place.

Going up through walls is easy, often just 2 small holes in the wall, one to drill the plate and and one for the cat, the cross piece between studs usually halfway up a wall. fishing in the direction of the joists is easy, going across them can be done with small holes spanning the joist, notching it for the cable, and then put a steel plate over it.Given that your problem unit is ground floor, it's likely you can fish up from the basement very easily for outlets using "old work" steel boxes, plastic boxes don't work with plaster on lath, it's too thick.

Thankfully plumbers are using pvc and other plastics these days so if you upgrade, you'll be upgrading to something not worth stealing.

I won't hate on that because my tenants have plastic/old chairs as well.

There are some really nice plastic laminates out there. 

The indirect tank was so full of tiny plastic shards I had to put a Y strainer on the output.

There was a fresh nick in the plastic pipe caused by them scraping the line against the box as they replaced the meter.

Bathroom has a plastic shower wall insert.