Isolation feet wouldn't be such a bad idea, just be sure your turntable is also well isolated, as there are stronger mechanisms at work in a turntable to pick up and amplify vibrations.
I can stand on a well glued wood base and it won't break, so I'm not sure there's a need to make it much stronger. You could add some small blocks in the corners to increase gluing surface. If you use corner blocks, you can add some holes in the corners of the top plate and screw it down into the corner blocks to attach them.