Mayor, If you have x amount of water vapor in a closed environment, then lower the temp, the humidity will rise because that volume of water is relative to the temperature. It's what is supposed to happen.
To make an adjustment, all you need to do is dry your beads so they'll have more capacity to gather water.
Take note that these changes are not instantaneous. It takes lots of time (read weeks of months) to bring the water out of the cigars and wood. You're not operating a microwave, ya know?
Incremental changes require time and patience. That's what you want, you don't want to change your RH rapidly as it's deliterious to the condition of your cigars. You want water to come out of them very slowly and evenly.
Lastly, colder air is unable to hold as much water as warmer air. It's a basic scientific principle that doesn't change regardless of how you perceive it. If you understand how it works, you can use it to your advantage. If you want me to help you lower that RH, drop me a pm and I'd be more than happy help you through it.
In your case, I'd lower the temp to your desired temp and then use Michael's beads or some sort of water scavenger like Damprid to pull that RH down where you want it.