I was wondering if I should do a chamfer or a roundover. For now, it's a roundover but I might change it to a chamfer for those reasons you mentioned. Right now it settles in snugly when I stack them.
I noticed the handle problem on the bottom rack when I was taking the pictures. After pics were taken I tried to pick up both racks from the bottom but couldn't get my fingers underneath to pick them up. I'm probably going to revise the design so that they all have the extra tall sides to give them a natural gap to pick up each tray.
Though I might cut a slot underneath the handles on the ends so that I can get my fingers underneath. I want the bottom tray to have a flat bottom so that if I put them on a poker table, the tray doesn't create a rectangle indent into the foam. The flat bottom helps distribute the load so I don't have to worry about denting my foam.