I'm thinking that the motion is caused by the coach being primarily supported by the suspension system on the axles. By transferring the weight to built in jacks you should reduce the amount of motion. I'm assuming you've checked the jacks to make sure they are secure to the chassis?
You mentioned dumping the air before leveling the coach, since that is the most obvious potential cause. As long as the suspension system is supporting some of the weight, you'll have some minor movement when walking around. I don't know if using additional supports (scissor jacks) would make that much of a difference, although it certainly can't hurt.