I think Vaughn's got it.
I'm in NW Washington, too. I use a similar method of pre-warming. An additional factor: some papers are especially susceptible to absorption of moisture. Ilford FB Warmtone is one. I've found that repeated gentle warmings rather than a single hot squashing may be necessary to keep the emulsion, which is soft, from sticking to the cover sheet. It's easy to end up with a defaced surface, but if sufficient care is taken, it can be avoided.
I have had this same result, and actually got rather good at removing the excess tissue carefully using a metal straightedge and a razor blade. The heavy bar the printmakers use, a "bevel bar," is best because it's heavy enough it's less likely to slip, but I've never been so fortunate as to have convenient access to one, so I use a good quality stainless steel graphic arts straightedge. Once the tissue is cut the full length of the print, it is easy to slip the blade under the tiny strip and lift it; it will pull right off.
Dry mounting still produces the best looking print, it seems to me. I've been trying NOT to do it in case my prints could be a resource for my family after I'm gone (how likely is that!), but I really don't like the way FB prints resist lying flat when treated as if they were etchings, etc.
Vaughn, do you leave a white border on your prints which is partially covered by the matte? I understand that air stains (those iridescent ones that we see on antique prints) begin at the edges and progress inward from there. Leaving about 1" of border around the print supposedly helps avoid that (but I ain't gonna be here when my prints start to airstain!).