Surprised you got lower action with the Hipshot being that it's pretty beefy to begin with. I think my two pointer on my EB-1 is getting curved in a concave way toward the body. Can it be straightened out and reinforced or should I think about a replacement?
It's a different situation than yours. The slotheads don't have an angled neck, so the neck has to be high enough off the body for the action to be low, and mine didn't quite get to where I like it (extra low). The Hipshot is beefy and its saddles are about the same height as the evertilt, but it sits directly on the top, while the evertilt sits above it even when screwed all the way down. That little bit made the difference in my case. Now it's 6/64" on the E and 5/64" on the G at the 17th fret.
As Rob pointed out on FB (when someone was looking for a solution to his tilting evertilt on a LP Triumph), the Hipshot needs to sit on a flat surface. Isn't your EB-1 arched where the bridge sits?
Waitaminnit, Uncle Dave gives up on his beloved two point - that wonderful, flawless bridge ... "if it had come with a string holder it never came with that is"!!!
Just because Gibson forgot the tailpiece is not a reason to blame the bridge.
As Rob also pointed out, a small screw placed in the center (laterally) under the front of the bridge will prevent tilting. I never had the problem, but obviously some people do.