Three things can contribute to moisture in the coop aside from leaks. Those are urine, poop, and breathing. Likely your vents are too small for the number of birds in there. Coop is very large so size is not an issue. I have 24 in a coop that is 8 x 16 and I closed all 4 windows tight last two nights. Had a little frost on E window, but other than that, no issues. My coop has ventilation as follows:
Two gable-end vents that are 12" X 12" ea.
One 18" turbine vent in center of roof area.
Two continuous soffit vents that are 18 ft long each X one inch wide, screened.
So the upper regions of my coop breathe constantly no matter if all four windows closed or not. All of my permanent ventilation is at a level of from 8' to 10 ft above the floor. The 4 large windows open fully for variations in degree of ventilation. I do clean poop planks daily and have windows open for at least two hrs. I do not heat tho, being in E Tenn. I have no insulation.
I would put your heat on a timer so that it is on only overnight. Open windows in AM when you clean coop. If you have poop planks, scrape them clean daily. If not, turn litter to cover poop daily. It is a constant source of both water vapor and airborne toxins. Close windows in late morning or anytime in afternoon . Complete air changeout is a vital daily chore, as important as food and water. For severe and lasting conditions, you may need to modify that schedule.