Mini Embroidery Pendant Help

I’ve been on a cross stitch jag lately, and would love to somehow turn my little creations into pendants. My finished cross stitch pieces are about 1″ square, and I’ve been trying to figure out a way to mount them into the bezels made by Sweet Beads “Fundamental Findings” since that’s what I have available to me. The clear domes that come with the bezels don’t fit because of the thickness of the cross stitch fabric plus the thread; however, the art still sits below the rim of the bezel without the dome. The uneven thickness of the piece from the threads in the back means that it’s not lying completely flat against the inside of the bezel, so I’m worried about it floating and air bubbles. I tried diamond glaze, but it reacted with the metal and turned the edges bluish green! It also created a surface that was sunken in. So, with all of that in mind:
1) How would I go about adhering the cross stitch piece to the inside of the bezel so it lays flat and prevents any air bubbles from getting trapped behind the piece?
2) What can I use that won’t react with the metal?
3) What should I use to encapsulate the cross stitch piece inside of the bezel, and how would I go about using it?

Just a disclaimer: I’m a beginner and I also live in Hawaii, so certain chemicals and products can’t be shipped here, which limits me to things readily available at craft stores. I’m also not totally stuck on using a bezel, so any and all ideas are welcome!
Thanks in advance!