Need some help removing some lock nuts

So, got our boy a foosball table for Christmas. When installing the players they have a hexagon shaped recess for the nuts. The idea is that you drop a lock nut in it, insert the bolt in the other side. Now the problem is that the plastic the players were made out of isn’t strong enough to prevent the nut from turning once the bolt gets halfway thru the plastic of the lock nut. So now the nuts have rounded out the hexagonal recess and I have no way of stopping them to either get them out or to tighten them down. I’m at my whits end. It’s also hard because all the rods are in place and I don’t have a lot of room to work. Am I going to have to drill all these sumbitches out?