Derekm, if I’m imagining this right, your swarm is in a box with a entrance under the hive? What is the slot size? I thought you were trying to achieve an open bottom area of around 12% before? Does your 2" bottom achieve that?
My original foam hives have 2” foam on all sides. Some with bottom entrances, some with tops. I still get bearding on hot days, but the bearding doesn’t start until much later in the day and then extends through the night. (There is a long thermal time constant with foam) That can be good, and that can be bad. It is good with respect to wax moths. No wax moth is going to get through a bearded entrance. It is bad though if a cold front pushes through at night with cold rain. A cold rain can kill a bunch of bearding bees. When cold rain occurs here, it seems to be most frequent at night.
In my hives, a top entrance prevents the cold rain issues, but it is going to lose more heat in the winter. Sometimes you just can’t win with bees