Interesting, and I can understand the frustration.
I don't know if this helps any, but here in VERY humid North Carolina, I have had good results as following: Like you, I store the cultures in the freezer, but I don't tape them closed. Instead, I roll up the package to eliminate as much air as possible, then bag the package in a small "ziploc" plastic bag, again rolled up to remove all air. When I use the cultures, I take them out of the freezer only just before using, and put them back (rolled and bagged) immediately afterwards. One tip: it is important to roll up the package so that one can see the label of what is in them. You can guess how I figured out that tip ...
Using this approach, I've only had one bag of cultures start to get a bit sticky/clumpy as I was getting close to using it up -- as I recall, it was a bag of Flora Danica. But I have never used any Biena cultures; most of what I get is Danisco, with an occasional packet from Hansen (all bought on-line from ArtisanGeek), so it may be that the difference has more to do with the brand than the storage technique.