I'm sorry, I misread your first post and now notice that the sheets are larger when they're still wet. That makes a lot more sense. What size do they end up being when they've dried again? What size differences do you note when dried taped to a sheet of glass vs. air-dried and then flattened?
As
@Lachlan Young points out it is inherent to the manufacturing process that the paper will shrink (and sometimes warp!) at different rates along both dimensions. In e.g. full-color gump printing, this is a problem, since registration of the multiple color layers will be difficult (impossible) to get exactly right through subsequent wet/dry processing steps. Gum printing is of course different from silver gelatin in that it generally starts with a different kind of paper than silver gelatin (although I guess it's possible to gum print onto fixed out silver gel. paper as well). Still, the paper base as such is conceptually comparable. Calvin Grier suggests for gum printing to pre-shrink the paper by soaking and drying it a couple of times, and during processing, hang it up to dry
always in the same orientation.
This method of pre-shrinking is evidently not attractive (or perhaps even feasible) with silver gelatin paper. However, I can imagine that it's possible to make a 'calibration sheet' that you print two sets of rulers onto, then process and dry it and observe the final dimensions of the image after the paper is fully dry and flattened. You can then use this final dimension to approximate an overall shrink/expansion ratio, and apply it to your production work. It'll never be perfectly consistent, but it may be good enough for your purposes. I'd suggest giving this a try. Otherwise, I think the only real option left is to let go of the requirement of trying to 'print into' an existing matte and find another way to present your images while making use of the existing frames.
From a moderator's perspective: we're all trying to help, and I frankly don't read
@Lachlan Young's posts as patronizing or otherwise insulting. I feel he's (admittedly somewhat assertively) expressing the inherent difficulty of what you're trying to do.