I shoot on public state forest land only a few miles from my house, and I use a plastic, folding table, and the plastic milk crate as my stool. I usually go with my brother and he brings his chronograph, and we use my spotting scope on a tripod to view the targets 100 yards away.
I can see why you're having an issue if you're shooting from something similar to a picnic table. For me, I need my seat to be separate so that I can adjust where I'm sitting in relation to what I'm resting my gun on.
You might try bringing some blocks of wood or anything else that you could use to raise your rifle up, if you continue to use the tables that are provided at the shooting range.