I've got a couple of alembicized basses (pickups/electronics), and they get close to the alembic tone. You'll hear the characteristic hi-fi and open E boom, but the meat isn't quite there when compared to a stock Alembic.
So, what I'm saying is that the Alembic tone comes from the combination of wood and electronics (duh, right?). I'd bet that you could Alembicize the right instrument, and get close to what you're looking for on a budget.
Otherwise, keep you eyes open for a deal on an Alembic. As a side note, I was talking to this dude, and he was all about the Peavey Cirrus as a close competitor to Alembic. I haven't played one, but his description made me interested in trying one. From what I saw, you could easily score one of those under a grand.
Good luck.