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I'd say a room that's of the proper humidity would be better than a humidified case for two reasons. One, the air can get even access to the whole guitar and two, there'll be no difference at all in...

That case will probably cover the fretboard too tightly. You could always do it in a garbage bag or cardboard box. Be creative.

If you're getting the clinks then your nut slots are probably fine. It's okay if the paper is tight, as long as it goes. All you're looking for is that the string isn't resting on the fret.
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I could see the hump right away in the first two pics. The fretting problem high on the neck that you mentioned is the dead giveaway though.

I'd prescribe 50%-70% RH for two weeks, maybe three....

Oh yeah - 40% - 60% relative humidity is ideal for acoustic guitars. Higher RH will cause expansion of the wood which will raise the action, deaden the sound slightly and a few other minor things....

Sorry I'm late to the party. I get lost in here sometimes. :D

Everyone's got good advice so I don't know how much more I can add. SVL's guitar is definitely seeing the effects of low humidity....