RNR, regular tarps, depending on quality, can sweat pretty badly. Canvas tarps are the best for covering -- they are $$$ but they really are worth it because they breathe and keep things dry while lasting a long time, which in PA would be worth it for me for horse-grade hay. Next year, I think I am going to put a canvas tarp over my moisture barrier, still pondering.
In your bank, I'd definitely put the hardware store moisture-barrier (it's a different material than a tarp, which you probably know, but I am good at the obvious) under your pallets, even if you have gravel. Assuming you have PA clay? Not sure how your bank is designed, but when there is moisture here, especially in summer, things that are under a basement-like bank hole mold almost instantly, blech.
It also helps, on your square bale stacks, if you didn't already, if you have a top single row of bales on their side to create a ridge, helps water/snow not pile up. You could do the same with a couple square bales on top of your round bales so there's not a flat tarp top.
I have envy for your tractor stacking!!!!! Next year maybe I can redneck a way to do it... I am already ticked at myself that I forgot to put my bottom square bales on their edges to help airflow, but I'm not unstacking it all to fix it now!