I liked the short tabs as it could stand up properly, but found it almost impossible to open.
This very simple change cuts a chamfer in to the end bin, which gives you an easy notch to get a grip on the start bin.

I've also halved the number of magnets which I thought was excessive.

And I've included a version with a D20 image cutout, I find it prints just fine without supports, easy enough to bridge. I've also included an SVG in case you want to mess about and add names.