I recently combined a weak hive with a strong nuc. I was dismayed to find that after a week the SHB were owning the place. There was no pollen patty involved. The SHB were thriving in the drawn comb that was light on bees.
Right or Wrong I removed the drawn comb that the bees were not covering, packing the hive down to just a couple of boxes. Each frame left in the hive is either honey, loaded with nectar and bees, or brood/eggs. I am hoping this will allow the bees to dominate all the frames in the hive, keeping the SHB population in control. I also find the beetle blaster traps work very well. This hive now has two of them.
The removed frame were left a ways away for the bees to rob out. They took all the honey and nectar, but left the pollen in the frames. Apparently pollen is not a precious as honey!
Today the hive is very active with lots of pollen coming in. I will check inside in a few more days to see how well this is working.