*sigh*
This is another one of those cases where what the customer wants is either not feasible, or just should not be done because it would damage the artwork.
So indulge me while I think out loud.
How large is this map? What kind of paper? Heavy, thin? If it's small and sturdy I suppose you could use clear corner pockets attached to the rear piece of glazing with spacers. But given it's a map, and antique, I'm thinking it's kind of larger and maybe on thin paper. Corner pockets won't work. And the customer probably would object to seeing them.
How about a few dabs of ATG, maybe even acid-free ATG to hold it to the back glazing? Sure, if you don't mind seeing big gobs of it later as the adhesive seeps into the paper. And as long as you don't mind ruining it, because that stuff's never coming off. And as long as you don't mind re-doing it once in a while as it keeps falling.
So, IMHO, two options present themselves:
If the customer can live with covering up a tiny portion of the map, hinge it and put it in a recto-verso mat. Glazing front and back. Gives better support, reversible, allows viewing of both sides.
If the customer has to see 100% of it and can't cover any of it up, Mylar encapsulation is the way to go. Then a recto-verso mat with maybe 1/8 inch or so between the window opening and the edge of the art. Glazing front and back.
Short of a magic wand and levitation, there's not much that can be done well without a mat while still seeing the back side.
Sometimes compromises have to be made, and you can't always get what you want. But maybe your client can get what he needs.