Thanks for all the excellent suggestions. Here's what I settled on:

I cut the hinges away and ground them down with a Dremel tool until they were below the contour of the triangle stock on the rudder and post. I then filled them in with balsa filler. Next, I covered over the whole thing with a strip of covering. The filler supplies support where the old slots were. Then, I cut new holes and slots 1/4" lower than the originals. So far so good.

Karl