I’ve seen it done with large portions of cloth. The basic process that I’ve observed is that you lay out a sufficient length of polyethylene sheet, layout your cloth on it, then saturate. Then using some form of stick, you roll it up on it, squeeze out excess and then go apply.
Here’s a video: https://www.youtube.com/watch?v=WdaPecHY4VQ
My experience was that those first two seams were the most difficult. The middle went off without a hitch, it was beautiful. But the Panel #1-#2 seams were a bit of a PITA. As others said, don’t fret it as no one will see those seams and there are things you can do after you start working on the galley hatch to make it look better where they might. And as you’ve learned, it is better to work in small batches. I had a helper mixing small amounts for me while I applied the seam. Just take your time and enjoy the process. 🙂