I did not, in truth, cure the problem. I just reduced the force element by removing the top from the post. This is a torque issue. Torque is force times distance. If you think of the post like the minute hand of a clock and the base as the point of rotation, with the plane of rotation parallel with the side of the motorhome, you can see that adding the top to the post will cause more torque, hence rotation, clockwise and counter-clockwise as the coach bounces down the road. The rotation is an extremely small movement, but it is enough to make the base and post sound off. Inertia of the table top causes the force, the distance is the length of the post between the base and table top.
Taking the top off of the post and putting a pad between the bathroom door and the door frame are part of our pre-departure nose management ritual.
Another source of noise was the facial trim on the microwave. The top of it was rattling against the wood it is attached to (with screws.) I backed out the screws a bit and put a shim behind the top edge of the trim, then tightened the screws.