Problem solved!
Thanks for all the great suggestions, folks. Unfortunately time is not on my side, so I needed to come up with a solution quickly. I came up with something that I think worked out well, and may be of benefit to others, so I'll post it here. The added bonus is that I can still remove the window insert, if needed.
Below is a picture of the inside of the box showing the clear, acrylic insert. Though they normally have a sufficient friction fit, this one will fall out easily (most likely due to humidity changes).
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What I did was fire up the hot glue gun, and using a toothpick, I applied a little glue to two spots on one edge, seen below. I then let it cool completely. Yeah, it got a little stringy, but I was expecting that. Just have to be careful not to get glue on the faces, although it is possible to peel of the glue if you mess up.
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I trimmed the spots of glue to about 1/32".
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I then laid the box down with the lid flat on the table. Pressing the edge of the insert with the two glue spots into the top part of the lid, I was able to press the bottom edge into the lid with a much better friction fit. The glue has enough spring to it that it holds the insert in snuggly. Since the two spots are at the top of the lid, and dry clear, they are virtually invisible. If you look for them, you can see the two bits of glue in the photo below.
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If you ever run into a loose insert, then you may want to give this a try. Thanks, again, everyone for all your input! :biggrin: