Hi Marybeth— Based on your description, your current environmental conditions are not terrible. The humidity is under control at 40% and the temperature is 55-60F. Even with some variations a little outside these numbers, your materials are doing pretty well. I am concerned about  your description of using deli type refrigerator units. These units will lower the temperature considerably, but will likely raise the relative humidity at the same time. The elevated relative humidities can lead to significant damage to the collections. You can prevent condensation on the photographic materials when you’re removing them from a refrigerator by sealing boxes and binders in plastic bags, but that doesn’t deal with the uncontrolled and potentially elevated RH issues inside the refrigerator. There are well-researched techniques for placing photographic materials in upright freezers safely by creating sealed packages for RH control. The National Park Service has a whole website devoted to it:

I have seen damage from photographic materials placed in refrigerators without sealed packages, but there are A LOT of variables, which I don’t think can be efficiently addressed here. You may find through testing that in your climate and with your particular refrigerator unit that you can attain acceptable level temp and RH levels given the correct temperature set point, but I would be concerned about the reliability of those levels. The experiences of people in different climates would not necessarily be applicable to your situation.

I’m happy to discuss my experiences with you by phone. You might also want to speak with the photograph conservators at the Harry Ransom Center, since they would be able to look at the situation in person.

Best,

Gawain