I am going to throw in a suggestion for Heartfelt beads. They are seemingly idiot proof, which makes them ideal for me. Nice two way humidification. Can't put too many of these bad boys in. They have kept my humi at 65-66% RH. David has excellent customer service and was more than happy to answer all my questions. www.heartfeltindustries.com These would really help with your excess RH.
If that doesn't look good, I'd second the Boveda packets.
Agreed - Heartfelt Beads are your solution, in my humble opinion.
In my cooler (not quite as air tight, but close), I find the best way to ensure the humidity does not creep up is with hf beads. I have the 65% beads, and for the most part, I leave them dry during the summer, and give them a little spritz with distilled water every few weeks in winter. Year round the humidity stays rock solid @ 66%. The benefit is that these beads both release
and absorb moisture, giving you the buffer you want.