Try a few in just Saran Wrap with no paper towel in the crisper drawer. Watch out for the back of the fridge. There are some cold spots near the blower where it may actually get to freezing. Just themselves wrapped tightly. Last year I had mold after 2 months in the fridge with a moist paper towel and a ziploc bag- no wrap.
Can also clean with antibacterial soap and a 10::1 water to bleach ratio or an anti fungal solution like Physan 20 from ebay. This helps to slow the growth of mold or prevent altogether.
I have all mine like this right now in the Crisper drawer and they have been fine so far. Just check once a month just to be careful.