There is a lot that can be going on here, right off look to see if the Gib moves up or down when your changing dirrections on the Z axis. If it moves any at all you have a problem. The slot cut in the end of the gib that grabs the screw may be cut to big which allows this movement. A new gib or a fatter head screw is needed to fix.
If it only has one ajusting screw ( with no locking screw on the gib like the X & Y) you want to move the head/Z axis down as you tighten up the Gib ( if screw is on bottom of gib). If its slightly bent this will help force the gib in far enough to be flat again. I have had mine get tight, but then do this and the gib goes in father which should tighten it up more but it really gets easier.
This is not the way to do it really but you can find out if the gib is not fitting flat real quick. Straightening the Gib, and sanding/scraping it flat is what is really needed. Even with a perfect Gib moving the head down while ajusting helps, but shouldnt be needed if its really right. If the Gib is not thick enough to take out all slack then a new one is needed.
You have to watch using the locks, this is what bends the gibs most of the time. Once the Gib is fitted and ajusted right the locks will not bend it as easy, but its still possible. It only takes light pressure when the axis is working right with a proper gib.
I suspect your gib is bent, and maybe even screw slot size not right. And flat means it will have full contact on the straight side, and the tappered side when checking with marking paste/blueing. Ofcourse yuo can check the flat side on a granite plate, but the tappered side has to be checked on the machine, while also making sure the flat side is fitting right.
But a quick try of moving the head downward as you ajust the gib may show some results. You should be able to take it to a point that you lock the axis up with the ajusting screw, but then back it up and all be good.
Ofcourse there could be a problem of the column not being exact and it having tight spots through its travel. Normally this would be the ends of the travel. EVen then you should not have this much clearance after ajustment and proper fitting gib.
Jess
GOD Bless, and prayers for all.