I was going to start testing glue ideas since there didn't seem to be that many options of plausible historical glues. But first, first, I figured I'd have a look at the history of wallpaper and see if I could find a little more information on Jerome Lanyer's 1635 patent to manufacture. I thought maybe I could find some more direction for what types of glues could be. I found Wallpaper,its History, Production, and Possibilities by Henry G. Dowling with a couple more clues about the early history of wallpapers. I did find out that Jerome Lanyer received his parent from Charles I on May 1, 1635 for a process he called "Londraindiana," and paid 10 (the book didn't specify 10 what) a year to keep the lucrative right to make flocked hangings. I found out that these were not printed on paper because paper wasn't strong enough. I also found the flock referred to as wool dust. I also found a date of 1620 for a French maker of flocked hangings called La Francois of Rouen.
From there I got pointed to a 1758 book on painting, enameling, and other techniques with recipes for paints,varnishes, sizes, etc, by Robert Dossie titled Handmaid to the Arts. There's an appendix to the two volumes called "On the Manufacturing of Paper Hangings" that is pointed to as the major source on early papers, including info on flocking. He discusses alternating large and small knives for chopping wool rags into flock as well as the use of a mill. He also talks about the application of the flock: "Flock requires to be put on with the varnish." He suggests printing the varnish then removing the hanging to another table "to be strewed over with flock that is later to be gently compressed by a board or some other flat body, to make the varnish take better hold of it."
In the earlier sections on the gilding of bookbinding papers and leather, Dossie also has some information that should transfer. He mentions that the size is put on a wooden plate or block rather than on with a brush. In addition to both gold size, he mentions that, "the size should be thickened with as much yellow ocher and red lead as the proper working of the print will admit." The size is applied to the block by setting it evenly onto a cushion that has been evenly brushed with size." This technique is an accurate discussion of the color sieve or color box technique that is used by modern block printers where a felt pad is saturated with color and then put on a stretched membrane that floats on some starch. This ensures even and consistent uptake of the color as you can't press too hard without the force being dispersed.
From Dossie I took a detour to The Grove Encyclopedia of Materials and Techniques in Art by Gerald W.R. Ward where I found the cool box for shaking the paper is a late 18th, early 19th century innovation and the earlier flocking would have been done with a longer staple fiber, and by hand. It also mentions the adhesive made from boiled linseed oil and letharge (that's lead oxide folks.) Back to Dossie, I find recipes for varnish and sizes. There's a glover's size which is boiled scraps of leather, making a gelatin glue that would be used warm too, but it doesn't quite fit the "varnish" definition.
So then I went off looking for suggestions on how to make boiled linseed oil without getting lead poisoning. I found Indra Kneepken's Master's Thesis for the university of Amsterdam. "Understanding historical recipes for the modification of linseed oil: An experimental study in the properties of modified linseed oil for use as binding medium in early Northern European panel painting". It is 150 pages of fascinating. That has sent me off digging through multiple Medieval manuscripts of recipes and back into Cennini as well.
I guess that's the long winded way of letting you know that I've gotten nothing done today but a bunch of reading? And my glue experiments are going to wait until I give this a few more reads and look up a few more references. I think the answer is here. Not as straightforward as "use rabbit glue" or "try some glair," but i'm actually very happy about that. i didn't think those solutions were going to work and this very well may. i like it much better than just grabbing a jar of modern glue off the shelf and doing that.
"Color and Other Materials of Historic Wallpaper" by Catherine Lynn, Journal of the American Institute of Conservation, 1981 http://www.cool.conservation-us.org/coolaic/jaic/articles/jaic20-02-003.html
Handmaid to the Arts by Robert Dossie, 1758. This link does not include the appendix, but there is a great deal of information on varnish and sizes that I am finding helpful https://archive.org/details/handmaidtoartsb00dossgoog