Ok, the feeling of the table wiggling is because all the weight of the table is basically on 2 legs, diagonally from each other, and the remaining 2 legs, diagonally from each other are barely supporting any weight. If the installer leveled the table side to side first, he may have gone to far on lifting one leg, then at the opposite end, raised the diagonal leg to bring it back to level. If you take a 3/4" open wrench and put it on the top nut at one end of the table, checking both legs, you'll find one nut turns easy, while the other leg nut is hard to turn. Check the opposite end for the same thing. What has to happen is loosen all the rails bolts, which will allow the frame to relax, and move the weight to the legs that the nut is easy to turn. Then you need to place a machinist level in line with the first diamonds on one end of the table, right in the center of the slate. Lower the tight nut down about half of what is showing out of level, then go to the other end, repeat that process, until the level reads level side to side at both ends, then tighten the rail bolts up again to 25ftlbs, then check level at both ends again, always adjusting by only half of what is showing out of level. Repeat at both ends until side to side is level.