when I designed this I made the boxes slightly smaller, so that they would not roll, but some thing I have done for other clients is use double sided tape, and stick it to a 1" x 1" plastic or wood, place it as far as possible inside the cubby so as not to see it, once you have place the bottle and you are sure it won't move, remove the other part of the double sided tape , repeat this step with another piece of wood on the opposite side, that should stop it from rolling. it works best with plastic, I found spacers at my hard ware store that worked like a charm.
hope this tip help

Thanks. I may do a similar work around with two short half round pieces of molding and some "quake hold" (museum wax).
Thanks!