I have had this problem of the table shaft being loose and wobbly at the base, it has a tapered chrome steel shaft that fits into a alloy socket and it just wouldn't stay solid, so on with the thinking cap (2 years later) and I have fixed the problem.
I got a length of 8mm all-thread, nuts and washers from the 'big green shed', then I drilled a hole in the alloy socket and assembled as per the attached sketch, making sure I put the washer under the alloy socket so it wouldn't crack it, fortunately the shaft already had a washer welded in at the top and I made sure I didn't over tighten the nuts, this assembly tighten the shaft to the base and worked a treat.
Hope this helps anyone with my model of motorhome or might even suit the JAYCO Silverline.