Re: PATB-3...?
The PATB series come with their own ring, but usually only a flat one. This will be most unlikely to be suitable for an R8. The other choice is to shave the inside of a normal ring.
I have had a PATB 3 in a Parker PM20, which is of broadly similar construction to a LP. It was too fat. I think a long scale bolt-on is the designated guitar for this pickup.
The C5 is usually the thin, bright and scooped one (of the custom family). If you say you like it then I'm thinking the guitar isn't necessarily bright, but that you're just looking for more drive than a PAF strength pup. In that case I'd second the choice of a Brobucker.