Just for reference: I've mounted a few pastels on museum board using rice starch paste. You can also use wheat starch paste or good dextrin glue. This method is completely archival and reversible, and what's best from my point of view, it's really cheap and can be done at home!
If anyone wants to see the procedure, I'd be glad to post it.
I'm not an expert by any means, but every art conservation site I've seen that mentions the subject expresses doubts about dry mounting and about all types of foamcore board, including the type that's sold as archival. Apparently foam outgasses in a way that may have deleterious effects. Dry mounting is not reversible and uses chemical ingredients that may degrade paper over time.
Now, I have no idea of the time scale we're talking about here. Of course things like ordinary matboard can stain paper in just a year or so, but that's the worst possible stuff around bar corrugated cardboard. I don't have the impression that foamcore is going to eat your work for lunch while your back is turned. I've often used it for a backing board when I'm framing pastels, though I always hinge the paper to museum board first. But I wouldn't permanently mount anything I wanted to keep indefinitely to a foamcore backing. (And you'd have to threaten to play Barry Manilow's greatest hits in an endless loop to make me frame a pastel right up against the glass, but that's a different story.)