As others said try the Baking Soda and if it doesn't work just change that humidors duty to Flavored Cigars as I guarantee if you spend enough time here a 40ct would only last you a month or two anyway. Trust me!
Find yourself a nice large humidor and have that one be strictly for non-flavored cigars. If you end of spending a lot of time here think about what size humidor you will realistically need and than times that by 4 and you should be fine for at least 6 more months.
I have been working at a local B&M part time a night or two a week and the problem you ran into is the exact same reason why when I have someone buying flavored cigars I always ask them if they also smoke non flavored cigars. If they answer "Yes" than I always mention that they should consider storing their flavored cigars outside of the humidor that they store their non flavored unless of course they don't mind their non flavored cigars tasting like their flavored collection. Most guys say they already do that while others thank me as they never realized or gave it any thought. The guys who never realized it I usually offer a water pillow to so they can at least move the flavored stuff to a big zip-lock or Tupperware.