I figure the OP got one of the BPCR type rifles that H&R made, with longer than normal barrels, and heavier than normal profiles.
The simple solution, as I see it, is to buy a new complete rifle, with a decent sized barrel to suit his needs.
As another fella stated, he got a 20G barrel with a .44 cal bore, so they were playing pretty hard with making what they had, cover a lot of eventualities!
My two best solutions are to buy what he like off the shelf, or to buy a replacement barrel that will work as an interchange with the original action.
I figure the OP has not really a good idea what the actual work might cost him. And though I cannot give a price quote, I am pretty sure a replacement gun is probably the answer, a replacement barrel may be, and a Re-bore is likely a third place winner in the general comparison of how to get things done!