I'd imagine a good pack that puts the weight squarely on your hips would work just fine. An ultralight/frameless type pack would likely be worse, as they generally split the weight between hips and shoulders.

It would seem that a good pack with a well designed hip belt, and the shoulder strap on the offending shoulder left a bit looser, could be made to work just fine. My suggestion would be to get to a local gear shop, and try on different packs loaded with either your gear, or the weight packs they generally have available. If there's an REI near you, they might be worth checking out, because of their very open return policy. If you find out after a few miles on the trail that it's just not going to work for you, you can always take the thing back.