Maybe the bottom should be fixed and the top removable. I’m sure it could be done in an attractive manner.
One way would be to put a frame around the top. One end of the mitered frame is not glued to the rest of the frame, but attached to the top which slides into a groove. When too is in place, the frame is completed. Seems like Derek has done this if I recall correctly. Just can’t remember on what.
I’m sure there are many other ways to do it.