First, it's not meat. Thawing and refreezing meat damages it. I have never had any problem with film. I often keep my bulk roll in my bulk loader. I take it out of the freezer and let it warm up for overnight or so. Load my cassettes, then put the loader in a plastic bag, drawing as much air out as possible, seal with a 'twisty tie' and put back in the freezer. I've been doing this for at least 50 years, and have had no problems.
40% RH is not bad. I can see that if the RH was around 100%, a lot of moisture could be trapped. My only caution is, seal in a plastic bag, drawing out as much air as possible, and, always allow ample time for warm up before opening the package.