Are you using OEM t-bars or did you upgrade to the OME t-bars? If you have OEM with the added weight of your rig the sway might be being induced by the softer OEM t-bar.
When I had the OME (101 and 133) which a buddy of mine has been using once I did my Fox conversion a couple years ago,they seemed, assuming yours are not blown, overdamped for the small bump stuff and underdamped for the large bumps especially noticeably after I added the weight of bumpers, AO drawers, etc. So I do wonder based on what you have presented here if indeed you might have a shock issue.
OTOH: If you are currently using the OME 865 spring: That spring suited me fine until I added the rear bumper and drawers (along with all the gear in the drawers ;-)...then they were as you describe with not as firm handling as I preferred.
Although there are a number of guys running the 866 spring I, as I mentioned above, didn't like it (more because of its short coming performance off-road than on-road).
I don't know how you, assuming you need firmer rate springs, will not get a firmer ride to reduce/eliminate your sway issue. But having said that the 863 IMO with appropriate ballast to suit is a nice overall compromise.
And lastly I did, after trying to figure out bad handling woes mostly noticeable over speed bumps or similar, Slee's adjustable pan-hard. It improved the rear suspension cycling issues I was having by about 75-80%. The remainder can be remedied by creating a pan hard mount that puts the panhard in a more horizontal plane ala stock.
One last thing: If you raised your rear suspension 2" I would suggest also lengthening the anti-sway bracket/rod length by a similar amount. I cut and welded mine with longer tubing but maybe Slee or ? offers them now.