That's really awackward that they burn like they should, which indicates -+ the right humidity, but you have some that are just too tight...
What's the humidity on the Island like? That might just be getting trapped in your humi long enough to do the damage.
When you open it, the humid air goes in, and stays in till the cigars absorb it... and the inner leaves over expand (maybe).
If you are not using heartfelt beads, I would suggest you pick some up, as they seem to be the easiest way to control humidity. Activate about 3/4 of them, and leave 1/4 just to absorb excess humidity, just in case it really is wayyy too humid on the island.