epoxy seems like a reasonable choice
Epoxies are really versatile and can give very strong results. It would have been the first thing I considered as well.
since there are some gaps of around 1mm width
Likely not an issue but most glues need perfectly mated surfaces for good adhesion. There are expanding glues, like Gorrila Glue, but most? epoxies are not meant to fill gaps. As long as there are sufficiently mated surface area this would be a non issue. If you do end up gluing it thick ahead of how the project will be sitting as it dries. Epoxies and take several hours to cure. If something shifts during that time you might be stuck with it (Ha I made a pun)
I am glad to see you already took some precautionary thought when it came to temperate and toxicity. I would have asked other wise if you had concerns about food safety. Some epoxies are food safe once cured and most have varying temperature tolerances. Read your product documentation carefully.
I used a cheap 2-part epoxy to repair the handle on my pottery mug that broke in 4 places after I accidentally threw it of my work desk.
Part of the handle shifted while curing, as I can see a crack (not very visible on the right hand side of the photo) that should not be there, but it has held strong for over a year now. The "crack" you see in front is a void because I could not find the chip the came from there.