According to Carvin's web site, they use an 8.25 degree angle on the headstock. Seems like if it has locking tuners, it should be able to stay in balance. If you're ever near Bellevue, take it to Mike Lull. He's a legend for good reason, and I would think he could sort it out.
My black strat has a 2-point trem and locking tuners. It originally had a Wilkinson roller nut, but I couldn't get it stop rattling so when I had the guitar refretted I asked the luthier to replace the nut with a standard slotted version. It's been MUCH more stable since then, which is counter-intuitive. When I restring, I pull the string pretty tightly through the post before tightening the lock, so once I get the string up to tune, there is always less than one wrap around the post. The locking tuners seem to keep the whole thing nicely in tune, even with vigorous whammification. During our versions of "Scary Monsters" and "Beauty and the Beast" I basically assault my guitar to conjure up those wild sounds, and it remains in tune.
:nightmare: :-x
