Do you want to embed components into a 3D print? Or are you looking to create a custom trinket box? Perhaps you're tired of rummaging through a jumbled mess of guitar picks. If so, this article is for you.
Interesting project, and I am sure you learned quite a bit while doing a fun project.
The failure cases are usually the ones that offer the most opportunity to learn.
At 6:00 minutes into the video, you are showing the “failure” that got left out in the sun and warped.
I am wondering, were the two materials (the green and the black inlay) both the same? My guess it that there may have been two factors involved, but both related to thermal expansion. The black inlay probably got hotter (absorbed more of the sun’s radiation) and so it expanded more than the green part did. The other thing is that the green and black materials may have been different and had a different thermal expansion rate, and that can cause things to warp too. It is used in old fashioned thermostats as well as analog dial thermometers, that used a spiral bi-metalic strip made of two layers of different metals that expand at a different rate. For example see How does a bimetallic strip thermometer work?
You observation that the non-embedded lids “stayed on” better is explained by how fast the magnetic force drops off with distance from the center of the magnet.
With thin magnets (thin between N and S) the magnetic attraction drops off rapidly. With 3mm x 1mm the effective “radius” between dipoles is 1/2 mm. So increasing the separation by 1/2 mm will decrease the attraction by a factor of between 4 (2^2) and 8 (2^3). As you get further the “far field” 1/r^3 becomes the “dominant” part of the equation. For a better discussion of why see Why does magnetic force vary in proportion to the cube of the distance instead of the square? on physics.stackexchange.com
If you made the holes a bit larger, or made a channel/notch for excess glue to escape from under the magnet, you could probably use something like epoxy to hold the magnets in, and once it “cured”, sand it flat. I have had mixed results with superglue. How well did the Gorilla Glue you used on the light repair on the van hold up? I don’t think I would use Gorilla Glue on the magnets. Here’s a page that compares different glues When to use Epoxy vs. Super glue and other adhesives
The downside is that using Epoxy is that you would need to do in batches (since you need to mix up a batch, of expoxy, and will only use a very small amount per “pick box”, and it would definitely take more time.than just inserting the magnets. So you will have to decide how important the lid staying on is.