How can Humidifiers work in Snug Cases?

I use humidifiers on my solid wood ukes, of course. I have 2 different types, both only fit in the top part of a hard case; in the headstock area.
On one hard case, the lid padding comes right down onto the strings. I'm wondering, am I only humidifiying the headstock? Is it possible for all parts of my ukes to benefit in this type of case?
(interestingly, this case has a hygrometer set into the accessory compartment - can it only read what's happening in the headstock area?)

Should I be looking at an 'in-uke' type of humidifier in such a snug case?

I would think the water vapor, in the state of a gas, would be able to permeate the area of the case even if it is snug. But, I am no scientist. Just an armchair observation. I would think that a humidifier in the body of the instrument would do the job better.

A humidifier in a hard uke case doesn't just humidify your ukulele, it humidifies the case materials as well. Most hard cases are wood costruction, which absorbs moisture and provides a stable envronment to its interior. The vinyl covering serves as a barrier trapping the moister air inside. An in-case hygrometer may show a difference in different parts of the case at first but after a little time closed, i think you would find that the wood case and wood uke have pretty consistent internal RH level.

I've personally experimented with humidification in both an empty case as well as with the uke in the case. I've found that there is quite a significant difference in relation to the distance of the humidifier and the the area you most want humidified. When I'd place the humidifier in the headstock area, the humidity in the body area of the case was significantly lower in both the tight case and the "airy" case, uncomfortably so. If I were on target for RH in the headstock area, I'd be below where I'd want it to be in the body area. I went with one of the Oasis humidifiers that go in the body of the uke and hangs from the strings so the humidity is going where it's needed most. I've placed a hygrometer in the body of the uke with the Oasis humidifier over several weeks/months and the RH is a perfect 45-50 degrees RH. I also have humidifiers placed in the neck area of the case for the head & neck of the uke. (one a home made, the other a Humistat) Based on my experience and experiments, a humidifier in the headstock or neck area of the case is not going to be effective for humidifying the body if you want to keep it at 45+ degrees RH.

+1 @mikelz777 - I have a case with a hygrometer in the head compartment. Moving the humidifier from the sound hole to next to the neck over the neck compartment raises the reading on that hygrometer by 15-20%. That tells me there is not much, certainly not enough, circulation from the sound hole compartment to the head compartment.

I now have the entire room humidified, but when traveling I will continue my practice of using two humidifiers - one in the sound hole and one in the headstock compartment (to avoid fret board shrinkage and sharp fret ends).

Edit to clarify: By raising it 15-20% I mean raising it from ~40 to ~60 - not from ~40 to ~48!

John