Beads might work, but I'd suggest getting a dehumidifier set up in your finished basement if you haven't already. That high of humidity could be troublesome from an indoor air quality standpoint and could allow the growth of mold/mildew, etc. in your home. Does your basement smell musty at all?
I aim for 60% RH or lower in my finished basement. I set up a dehumidifier with a hose running into my sump pump so I don't have to empty the reservoir every other day. I would pull the hygrometer out of the humidor for a night and see how high the RH is in the room.
And, FWIW, my end table humidor is also in my basement. I have very little trouble maintaining 65%, only needing to address my humidification system (partial active (Oasis) and beads (HCM)) monthly, at most. During the winter I add DW approximately every two weeks.
Good luck!