Ernesto, there is no basement. The "crawlspace" is just the underneath of the house. It's one of those raised houses up on little concrete triangles. It's basically just dirt a couple feet below the plywood. The same moisture barrier stuff was used in my bathroom and saved the lower part of the subfloor because it was between plywood sheets. But, if you think it's a bad idea, I will skip the moisture barrier. The vinyl plank manufacturer did not say any moisture barrier was a requirement on wood subfloor.
Nick, That's a good idea. My primary concern is if something happens with the hose & it doesn't land in the pan or if my incontinent dog pees on the floor.
I've been thinking about the subfloor situation, and I've seen that there are some types of tongue-and-groove flooring grade plywood that only require one layer to be put down (but I think that is with 16" spaced joists). So, I'm debating if it would be easier to build in additional joists (which would also allow me to level things up a bit more. I could sister up to some of the existing ones and add new ones in between at the right intervals. That way the floor will have extra reinforcement for the washer & dryer & tub. It would simplify the process of alternating the seams as well. In the long run, I think it might be easier than trying to mess with 2 layers of plywood, and I can use construction adhesive on the joists to keep hold the subfloor steady to limit movement.
I was watching the old video of "construction Mr. Rogers" (not what he called himself in the video, but what youtube viewers called him) and he mentioned maintaining a 1/8" gap between the board ends that did not have tongue and groove. So, should I have a gap like that? I saw that someone who used 3/4" tongue-and-groove used ring shank nails that came with adhesive on the shanks to hold them in. I don't know if I've ever seen those sold around here though. If they are, I wonder if they would work in one of my nail guns (although I would still want to reinforce with screws).