Update: Okay, found a solution thanks to a bunch of helpful posts. It requires a pretty detailed understanding of the game’s temperature mechanics, and relies on vehicle construction cheese.
I still think reducing the pod harvest time isn’t a bad idea, for reasons stated above. But I must concede that a novel solution does exist as of 10847.
Edit: In fact, dunno how I missed this, it actually takes 16 pods to build the first part of the shack, 17 for the next, and another 14 to complete it. I doubt anybody is even going to bother. 47 is more than you can find in a single tower, if my experience is indicative. It’s simply way too much work. Moreover, the second upgrade takes much longer 24hrs+, and man am I glad I went ahead tested that with debug tools.