I have never done a cinnamon roll in a mason jar so I didnt comment ~20 hours or so ago. Seeing as no one provided advice I figured I would make an attempt to help.
I recently did mason jar cakes for a summer wedding that had a country theme and used mason jars. The cake I made was a yogurt cake (after baking topped with sliced strawberries and topped with honey whipped cream). I poured in the batter using a funnel to keep the batter from getting on the sides. I put the jars into a cookie sheet with sides (a cooking pan?!?), and then filled the pan with water. I put this inot the oven. The water help keep it from burnt. I would try this jar/pan/water method. Also you might get good results from short mason jars
Good luck!
There are short widemouthed mason jars, perfect for looseleaf and pipe tobacco (just don't get the two mixed up).