I would try and bump that cool side up. I generally dont let the temps get below 75F. If your cool side is that low, you probably can leave the hot side around 88-90F to compensate a little. Thing is you dont want it too cool AND humid. That can trigger an RI. Just like hot AND too dry can trigger an RI too. Maybe put a little 40 watt CHE on the warm side to bump up the ambient if you are using a tank. You can then cover the cage top with tin foil and just leave a little space around the CHE. You dont need a ton of air flow. Thats what i do with my GTP cage.
And as for the Zoo Med hydrometer, nothing wrong there. I use a Zoo Med digital temp/humidity unit for my GTP up top and have an Acurite on the floor. They both read about the same so unless both units are off by the same amount, they seem fairly accurate. Also with humidity, you dont need to be EXACT. Just in the ballpark. Honestly, the best sensor i have found has been my nose. When i open the cage, i just stick my face to the door and you can feel the humidity especially if your house is like mine and sits around 35% humidity lol.
I think if you throw in a little CHE on the warm side to help bump that ambient up and then cover the whole top of the cage except about an inch or so around the CHE dome, you will be fine to just mist with a hand sprayer once or twice a week especially if you are using a coco fiber substrate.