With the mason jars, the ingredients didn’t remain evenly distributed during the cooking process. In addition, the egg bites didn’t slide out of the jars, although I coated them with cooking spray as instructed. I treid this method twice.
During my research, I found a recommendation to use a Weck jar. But water leached under the lids.
Finally, I decided to try the silicone mold. I have no way to determine its mass measurement and I could only find one recipe which is the one I followed before posting.
Following my post, I put the mold back in the 187 degree water and added 30 minutes to the cooking process. The bites cooked through but still weren’t firm. Your suggestion to increase temperature and cooking time sounds right, though.