1 month update: Still going strong! No catastrophes yet ;)
Print on side as shown, no supports. Highly recommend printing with PETG, but if you only have PLA, I've included some notes below.
Jar may slide down and rest on brim if heavy enough. Might benefit from some tape on the inside of the clamp to add more grip.
Obviously, watch out. Mason jars can break and spill glass everywhere so be cautious of where you place them in case the jar falls.
If using PLA:
After printing, carefully stretch the clamp to loosen the material. I like to clamp it around a mason jar overnight before mounting. This will help prevent shattering. I haven't had that issue with this version yet, but better safe than sorry.
The author marked this model as their own original creation.