We all have dealt with flipping the bike upside down and pushing/pulling the wrench to torque the nuts. It isn't a problem.

I will try to be helpful. let's see
1) try screwing the nuts all way to the frame before centering so getting them tight doesnt take much turning
2) center the wheel - easy because you have the built in centering screws
3)get the nuts finger tight and double check the wheel is still centered and chain tension is how you like- adjust centering screws and wheel as necessary
4) take your wrench and tighten both nuts evenly. Evenly, meaning screwing one side a little then the other until they are both sufficiently tight

assuming your track nuts are good you shouldnt have a problem