It's very likely to be a different sound (maybe not hugely so, but distinguishably so), since presumably (a) you'll use non-carvin p'ups, and (b) you' might choose some lumber Carvin doesn't offer, and (c) you'll recognize the construction of the Warmoth L5S is going to differ significantly from the set-neck Carvin. My guess, however, is that you'll get into the Warmoth for a pretty penny, too, so you'll feel cautious with it just as you feel cautious with the Carvin. You could easily drop a grand or more on the body and neck, if you get a swank finish and some sexy lumber - and then of course electronics and such will put you further into "oh my god it's so expensive but I can't deny myself" territory.
If you want to duplicate the Carvin as closely as possible, I think you're looking at mahogany back and figured maple top; but why limit yourself? How about some sexy black korina, or get really out there with a wenge or cocobolo top?
Have fun, anyway. I'm jealous of your SH550 - they're very pretty guitars.
Bagman