You say you replaced the seats. The seat is where the usually rubber washer on the end of the stem seals against the back of the valve body. If you put your finger in the hole where the stem goes you should be able to feel the surface where sealing takes place. This surface can get scratched and allow leaks. In fact, the leak can make the scratch worse over time. Also, debris can become trapped in this space during repair and prevent sealing. So, make sure the seat is not scratched, it can usually be replaced if it is, and make sure no debris is left behind before closing up. Additionally, there is usually a washer made of paper fiber or hard plastic that sits between the valve body and the stem above the threads. If this washer is worn or missing leaking can occur at that point.
Finally, you say you replaced the seats and it got worse. It is possible the seats are not tight or are installed incorrectly, crooked, or cross threaded preventing the washer from seating. Check for that.
Good luck!
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. ;)
Best Answer
There are seals inside the diverter which can be replaced. This may be an O-ring or a more complicated seal. Turn off the water at the valves. Unscrew the diverter stem and take it to a homestore or better to a plumbing supply.