Can you ID this shower system/panel product?
The answer: Swanstone

How I found it: I got lucky. I just grabbed it and started taking it to local big-box places (I assumed it was a big-box as the materials in this house aren't necessarily 'high end'). 

I stopped at Lowes and the initial guy in the kitchen section had no clue, but I was fortunate that a curious co-worker popped his head over the counter, thought for a minute, then declared it 'Bermuda Sand' from 'Swanstone'. We found the swatches and, sure enough, he was right-on. So kudos tot he very helpful Lowes employee.

Apparently, these type of shower systems are just large panels of solid surface material that is glued up on the wall. They idea is that the panels abut, then caulked. The corner cove is more of an 'extra' piece that can be used if desired. The underlayment SHOULD be your standard tile surface...water proof cement board that is then sealed with some sort of water sealant. However, I don't know that in this case, so this particular piece seems to be a rather critical for my shower. So, glad we were able to find it. 

The challenge for future people reading this is that I guess the solid surface companies are many, and the patterns all tend to be unique to each company, so it is a bit of a needle-in-a-haystack hunt trying to find these.

For contractors, I'd like to suggest leaving a note on the inside of a bath or kitchen vanity with the manufacturer's info. That'd be handy. ;)