Reduce high humidity in attic
Yes, 70% RH is too high for a 36 degree attic. And your advice is on the money: stop humidity from entering, and remove humidity from the space.
First, add vapor barrier caps to the lights, seal the hatch opening, and use duct seal or tape on all the ducting.
Second step, get some air changes happening. You could install an attic exhaust fan towards one end of the space, and put an intake grille at the opposite end.  The fan can exit air through a soffit vent, a gable vent, or a roof jack. Wire the fan with a line-voltage dehumidistat mounted in the attic not too close to the hatch.