The quarter inch was too much...with the gap on the corner and the unsteadiness of the top box, the bees were flying out the sides. I'm pretty sure this would leave them wide open to robbing and also leave some room for burr comb.
If I use weights on top, what I would be doing is warping the top (empty) box to fit the warped (full) bottom box...that might make both boxes unusable for interchanging later, not sure. What does sound good is the shimming ideas and then tape up the distance, I'd just want to be sure not to put any of the "sticky" towards the inside of the gap where the bees would stick. We are having high winds and rain for today, so the girls will have to wait at least one more day...I sure don't want to chase down any more swarms! All the ideas are great ones and definitely giving me some options I would have never thought up...I'm always open to creative ideas and usually I'm not too good at that!
Still not a problem. Lots of my boxes have corners out and other openings. A decent hive won't get robbed out in a 1/4". Your entrance is far larger. I also prop tops up.