And I say: Don't take the strings off! At all. Leave them as is. Period. Do only when doing maintenance! Your pics are demonstrating that very notion. Your pics have a top headed bullet where it is very easy to adjust truss rod, but if the adjustment is in the heel only, you bet that people will leave it, because it's too - way too - unwieldy to loosen that truss rod from that end.
(weeks, months or years depending on climate)
Yes, you said the magic words there:
depending on climate. The thing is that most people doesn't think it has to do with climate, and then make up their own minds and trying to find bizarre and DIY reasons for it, that it must have been the strings tensioned up all of the time. They can't think of something else.
I challenge anyone to a double blindfold A/B test any day. Leaving a bass in it's case with all strings off and all strings on. And take them out after a year. Mind you it was that WIKI I pointed out, where it says absolutely nothing about adjust the truss rod accordingly when taking off all strings or even slacking them.
It's the same as if the neck should warp if you happen to inadvertently put lighter gauge or heavier gauge strings onto your bass and not adjusting the truss rod for perfect relief. And that something should happen in the long run with this. You can wait 10 years and think, all of a sudden "oh, this neck has a bit too much relief due to the added tension of the heavier gauge set". Belive me it will follow accordingly and adjust itself perfectly. Or the other way around, you put super slinkies on the bass for thumb slap, a 030 set, and it's buzzin but you don't notice it since you have too high action. And let it reside 10 years like that, hanging on the wall or stand mind you, not mothballed. You can detect the backbow and adjust the truss rod. What would you think if a truss rod didn't do anything? Stuck for one gauge (or really: tension) one-size-fits-all?
Now, if the adjustments doesn't do the trick then, it's only because of climate as you said, huge and fast variations in humidity/and temperature. They more often than not goes together hand in hand.
I have seen, and owned numerous old acoustic guitars without truss rod even, and they fare well. With strings on or without. They're made so sturdy and of good raw material that they wont shift whether being left with or without strings on. No truss rod to adjust at all, as it was with basically all Martins before 1989. Now, I particularly don't like guitars or basses were I can't change relief and it's set in stone what types of string you're going to use (or really:tension). I've seen archtops that I can put on 016 set (a la Pat Martino style) as well as 008 set (did it just for checking) and nothing happened to the neck at all. Even in the long run. Things made of the right stuff. They had NO truss rods, let alone adjustable.
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If you can't take off all of the strings for maintenance, and your neck is flexing back or forward to a state which it can't retract from, it's a bad bass. Or bad neck really. Use it as a dumpster find. Log on the fire. That half an hour it takes for changing strings it should be able to cope with.
The only thing that will happen with long term storage, is that the strings will still have metal fatigue, and the stress from being tuned up to pitch
may cause them to snap, given long enough time, without touching them. 4 years 10 years. Strings have shelf life too you know. Past date.