I've tried searching and nothing recent is coming up, was there or was there not a thread regarding neck-dive and straps (or other changes) that can help alleviate such issues?
I was thinking more along the lines of duct-taping some weights into the top cavity since there's now nothing in there that can be interfered with by doing so.
Another option is to extend the top horn with some type of hook which extends to the 12th fret or so. On my Strat, which was neck heavy, I solved this by getting a steel block, which was 12oz heavier than the block that was in there.