Whether using JEI to auto-fill the items or manually placing them in the crafting table the ring will not craft.

Partially charging the jetpacks in the recipe allowed me to craft the angel ring.

Given that charging the jetpacks lets you craft the ring, the issue is probably an NBT mismatch. Recipes customized with CT are very particular about that.

I've also experienced this issue. You pick up the ring from the table then it rubberbands, uncrafting itself back into the ingredients in the table. I had to cheat in the ring and delete the components as a workaround.