Ok, first off, try drying your paper on some plexi. Just transfer it from your screen to the plexi by pressing it on then sponging all excess water then peeling the screen off.
Also, don't let it get to thick, on good dunck in your vat should be fine to cover your screen, if you are seeing spots that are not covered you can do two things:
put the sheet back in and try for a smoother pull
or hand cover the spots with peices of paper pulled from the vat.
If possible let...