Hey-
I don't own a EB, but I happened to read a thread on the bass forum that might help. Guy there was looking for ideas on what to do with a EB style body he got from Warmoth, Anyway, someone mentioned how neck heavy EB's are, and the factory solution was to put the upper strap button on the back of the bass to improve the balance. An alternative was to move the strap button on the end(bridge) of the bass. Basically, it sounded like moving the one on the end would shift where the weight is distributed better than moving the one on the back of the body, and make it hang better.
Course, I'm guessing the neck keeps dropping and that's what you don't like.
If that's not the problem well... nevermind my babbling.
Bob