Heating also dehumidifies.
We have an airing cupboard with the hot water tank in it, and that is enough to make it a very effective drying place – we put our smalls in there on a rack on the back of the door and they dry out in no time. It’s warm in there, but not particularly hot.
So what I’d do is fit a plug in it and an oil filled rad. You’d need it on fairly low I reckon. You do need some ventilation of course, but in ours leaving the door ajar is enough. I’d be tempted to maybe find some kind of low speed extractor fan for the roof of the cupboard if my house was prone to mildew, with a vent in the bottom of the door. Fan should be very very low though. Maybe I’d make my own out of a PC cooler or something.
EDIT so after reading your OP, that’s option 3 🙂