Dr. Lin and I discussed this on Forum Friday, and I forgot to post the follow up for. I apologize for the delay.
There are some different strategies worth trying. Applying a protein barrier to the bun before applying the sugar topping is one possibility. This can be egg wash, egg whites only, or use a wheat protein isolate in solution. The idea is that the protein will gel and form a seal preventing the moisture from migrating from the bun to the topping.
Also ensure the products have cooled completely before packing. Do an internal temperature check to be sure.
The only other thing I can think of trying, would be to replace half of the powdered sugar with extra fine dextrose powder. This is used in donut sugar as well, and may not absorb the moisture as easily as the sugar does.
we hope this helps you, and please let us know how you make out, and if you have more questions or information to add.