Thanks for the tips. I found a bolt long enough to get it up a couple of mm, so I knew it worked. I dropped a long but small screw down head first then put the bolt back in and screwed it down and the posts came straight up.
A couple of seconds with a stepper going real slow and the posts are countersunk. Now to see what happens with the strings on...
And... that looks much better. It'd be really nice if I could keep the action that it just restrung at, but I suspect I'll need to come up slightly. So far, much improved.