Never installed a high hat? The joists have nothing to do with it. He's
between the joists. The high hat is held by clamps that grab the
sheetrock. His clamps are for a 1/2" thick sheetrock, but he has 3/8"
sheetrock. He needs a 1/8 spacer sheet.

I think your talking about the old work hi-hats for existing ceilings,
in which the tabs grab on to the sheetrock. I actually gutted my whole
kitchen, so the hi-hats I'm using are for new construction and are
held between the wood joists.
In any event, I did try one hi-hat up between the joists. Then I
carefully put my hands on the entire assembly and pushed upward
slightly. That did the trick, all I needed was an 1/8".
Like some suggested, I could have cut off the tab piece, or mortise
out the bottom of the joists, but I got 8 hi-hats to install
and it was just more easier what i did.
With regards to using the 3/8 sheetrock on the ceiling, this is my
opinion. Before I gutted my kitchen, I had the original 3/8 sheetrock
on the ceiling and even after a roof leak that went undetected for a
while, it never sagged. I could understand if every ceiling in my
house sagged, I would be reluctant to use it again, but to be honest,
my ceilings and walls look great. So this is why I decided to stick
with 3/8". Not because it's cheaper or lighter. It just made sense to
match the existing work. If I did a complete gut of the entire 1st
floor, that would be a different story.
By the way, I am putting in a vented range hood that helps out the
moisture situation.