This is an honest question: can the additional weight in a Bikini be held by the wooden legs? Even with the double anti-split bolts in the bingo legs, it's a LOT of weight. I do not recall which was the first bingo with metal legs - I'd guess it was Lite-a-line (as the first with metal rails). If that was the case, can the earlier/any Magic Screen games be held by wooden legs?
It sounds like the easiest answer to your problem is to get another game.