There's absolutely nothing wrong with providing plenty of air circulation when curing soap, but I wouldn't stress out about it. Soap loses about 10% to 15% of its original cut weight during the typical 4-week cure. Based on the tests I've done, about half of that water is lost in the first 10 days or so. The remaining water is lost more gradually, so lots of air circulation is not nearly as important later in the cure period as it is at the beginning.
If you can keep fresh soap for about 10 days in a well ventilated environment that would be good. I would have no problems after that time about moving the soap into a storage area that isn't air tight, but with considerably less ventilation, like your chest of drawers. That's pretty much what I do. I cut the bars and store them in shallow cardboard boxes that are lined with clean cotton toweling. The soaps are covered with another layer of toweling to keep the dust off. I give the bars a week or two to dry in an airy open place, and then my soaps finish curing in a closed cupboard. The boxes are loosely stacked in the cupboard, but I don't use a fan or keep the door open or anything. They do fine.
After 4-6 weeks, I package the soaps in shrink wrap. They continue to lose weight for months even after shrink wrapping, so it's pretty clear to me that soap is tolerant of different storage methods.