We run a Chevy 2500 long bed non-4x4 and a much heavier camper. With the overloads just touching, the camper feels just a bit top heavy. I added a Hellwig sway bar which eliminated most of the sway. Made it very comfortable to drive.
You said your sway bar made no difference. I would be concerned it wasn't installed correctly. You should feel some difference even if it wasn't a very strong bar. I think the Roadmaster is a heavier duty bar than the 1 1/8" that I have.
If you want to increase the overload tension without spending so much, look at the Energy Suspension products. They have rubber spacers that will fit your overloads for about $30 for 4 on ebay. There was a conversation last week concerning these. You might search previous posts.