It would be risky to rely on any sort of adhesive or coating on the puzzle, because it probably could not resist deflection or disintegration in the event of impact or pressure on the front or back. The surfaces would be vulnerable to damage from light, soiling, abrasions & scratches, too.
The glass sandwich is nearly always a bad idea, because glass is a poor thermal insulator and condenses moisture readily. Google "Dew Point" or search the archives here, and study. When you understand how the natural phenomenon of dew point works, you will understand why a glass sandwich mount can cause mildew, mold, and stuck surfaces. You will also understand why it doesn't always happen.
Sandwich the puzzle between two sheets of acrylic instead of glass. Acrylic has half the weight and twenty times the shatter-resistance of glass, and it is a much better thermal insulator - less prone to condensing moisture, so the dew point condition is much less likely to occur with acrylic.
One drawback of acrylic in a Direct Contact Overlay (DCO) mount is that the item in direct contact might eventually abrade the inside surface of the acrylic. The answer to that is to use abrasion-resistant, type AR acrylic. UV filtering is always recommended, as well. Specify Acrylite OP-3-AR. Or, if the budget allows, use Optium Museum Acrylic, which has the additional benefit of optical coatings for higher clarity and anti-reflection.
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