Try a warmer iron, on the dampened jacket (maybe a damp cloth rather than a mister?), with a sheet of clean paper between the iron and the jacket so the iron is not in direct contact.
Try a back corner first and see how it does, and make sure no ink transfers to the clean top paper you are using. If it looks good, go!
I'd not use the inner sleeve in any condition. I use the MoFi Original Master sleeves but save the original jacket if it has lyrics and/or art I want to keep. Plain ones get tossed.
"Just because I don't know what I'm doing never stopped me before!"