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. ;)
Moentrol is the type of valve, the single knob that pulls out and pushes in for flow control and rotates right and left for temperature control. There were numerous trim styles offered with that valve type, so just saying "Moentrol" does not adequately describe your needs. Some of the old trim plates were marked with the word Moentrol, but many were not. If you contact www.lasco.net they will direct you to a dealer. They have a huge line of plated trim in all finishes (ask for the Simpatico line) at reasonable prices and of good quality.They call it Satin Nickel but it looks like brushed nickel. You might need to take your old trim to the dealer to ensure proper size/type, rather than risking an on-line purchase.
Best Answer
Unlikely.
The new one has a square ferrule, yours is circular (hexagonal?).
You would need to get the escutcheon cylinder off of the new one and it would have to fit the old (or reuse).
If I had to guess, the new one pivots and rotates, where as yours just rotates. The action on the new lever seems to me like it would be un-ergonomic, if so.
Swapping out just the cartage might work, but I've no idea how to do that even if it's possible (and you'd be one lucky sob if you found them easily interchangeable). I've never tried to repair one with non OEM parts.
I also see no means of attaching the new escutcheon plate. Caulk is supposed to hold it, eh? More things I don't like: square handles and plastic ferrules. Whatever you do, Do Not discard your old parts, or you might be sorry.