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My fiance, who is considerably craftier than I am, suggests Tombow MONO Adhesive Permanent and Tombow Multi Liquid Glue (both of which she's used for scrapbooking) with heavy cardstock and metal letters, though she notes her letters are probably not as think as yours.
She also suggests you take a look at Tombow Mono Adhesive Power Bond.
Magnets behind the letters is really a great idea. That's what I would do...as well as archival safe acrylic glue. Card stock is also your best bet, regular paper will wrinkle from the weight.
Stainless Steel is generally non-magnetic. Magnets might work if you could paint the backs with an acrylic paint loaded heavily with iron filings, but that opens the door to oxidation troubles.
I'd try 3M "Super 77" spray adhesive, which is not super-permanent but might be enough to hold under glass. Or try contact cement on both surfaces, applied with a roller. Remember that with any adhesive, impeccable surface cleanliness is 90% of the key to success.
Long-term, it might also help if you can laminate your paper to a foam-core backer, or otherwise add structural stiffening. You want the adhesive to be working against the shear forces of gravity, rather than against the peeling (shear + lift) of a non-planar backer.
In fact, if you could use foam-core in back, you could use 5-minute epoxy to glue some pins or brads perpendicularly to the backs of the letters, and just push them into the foam like very fancy thumbtacks. Pretty cake, BTW!
I talked with She Who is Crafty, and her opinion is that you should (if possible) stick with cardstock; it's less likely to wrinkle or tear under the weight of the metal, and will last longer, whereas regular paper will yellow and fade reasonably quickly.