Me thinks you are over-thinking this. An air 'conditioner' conditions the air by REMOVING moisture from it and then cools it by blowing inside air over the cooling coils. When I run my a/c in humid conditions, the water (condensate) is quite visible as it runs off the roof and down the side of the motorhome. If this isn't happening on your unit, I would suspect a problem with the a/c. But since you say the air temp is 70 degrees, I would think the a/c is doing its job. If you feel the a/c is not removing the moisture sufficiently, I would invest in a small dehumidifier.
As for the storage spaces that do not receive conditioned air, Damp Rid would be a solution.
Also, today's refrigeration units of any kind no longer use Freon.
