My computers have not been functioning well enough for me to make progress on any sets lately. It's been really demotivating... But I've turned a corner and have been gearing up for making a new set. While cutting the foamcore bases for tiles, I had a thought. The 6" tiles have enough space in them to cut out a 3" tile and leave behind a sturdy edge.
I did a test tile, and the results seem pretty good. Though you can clearly feel that the center is hollow, it's sturdy enough to hold props or minis. I think I'll do this with a dozen or so pieces and see how they hold up to some actual use. Here are shots of the front and back of a 6" tile I did this way: