Sounds like you need a utility razor to cut those ground sheets. Assuming you can buy one without being considered a dangerous felon, of course. And I dunno if I’d try it on something as thin and cheap as lattice wood, but an old carpenter’s trick to keep from splitting the wood you’re nailing into is to tap the point of the nail with the hammer before you set it, to blunt the point. I can tell ya from experience, that one works.
I gave up on trying to cut the ground sheets and just built shorter screens. I’ve been doing the blunted nail bit, but even that was causing splits. The wood is just mealy. So I’m drilling their holes about halfway. The problem is, aside from the quality of the wood, that the lattice framing has such a large stepped channel carved into it ( I gather lattice must come in several thicknesses ) that there isn’t much wood left. Try putting 2 finishing nails into the end of a 1/2” x 1/2” piece of pine, you’ll see.
Well as I said, I dunno if I’d try it on anything as cheap and thin as lattice wood. I’m not surprised yer having to drill pilots.