new monitor
So, while talking with my manager about some of the things we were trying to do to address this (our build manager, in whose lap all this falls, has been wonderfully helpful), my manager said "I just ordered some new 22" monitors; I'll put you on the list". (I could, if I like, have a pair of 18?" monitors, but I can't actually place two monitors such that I can see everything.)
This morning the monitor fairy came. :-) 22" turns out to be widescreen (not the 4:3 or whatever of regular monitors); the new one might be half an inch shorter than my old one. But it's tall enough, and the extra real-estate is nice. The recommended resolution is only 1680x1050 (or something like that), which surprised me. (I expected to see a number over 2000 for the wide dimension.) That resolution actually works for me; yay! This was also the highest setting available on my computer; I assume that's a function of the graphics card and not the monitor. (I would not be able to put higher resolution to good use.)
One problem: I noticed some pretty significant color distortion in the top quarter of the screen. We actually thought it was defective, so we swapped it out for another one (slightly different model). The problem was less pronounced on the second one but still there. That's when I noticed that it changed with my height; if I raised my chair a couple inches the problem got much better. But I can't raise my chair a couple inches because then the keyboard will be in the wrong place. (Tried it for an hour. No.) If I could tip the monitor forward a little that would make a difference, but it's already at the max setting there. Perhaps I will channel my inner MacGyver and rig something to let it tip a bit without falling. (Ok, that's more like my inner MacGyver's four-year-old apprentice or something. MacGyver would rig it to track my eyes and auto-pivot in both dimensions, using nothing more than duct tape and pocket lint.)
Mind, I will find ways to live with the color distortion if necessary. The real estate is worth it. It's not a perfect solution; I have to roll my chair sideways a bit to fully utilize the screen. But it's pretty good, and if it just plain gives me the room to have some extra-wide windows that I can move around as needed, that'll do.
I failed to record my monitor customizations before removing the old one, so I was recreating color depth, brightness, etc by feel today, but I thought I'd written this down somewhere and, sure enough, I did. So I'll try those settings tomorrow (they're somewhat different from what I came up with today) and see how that affects my color distortion.
One other problem (handily solved): the first monitor did not have buttons but rather touch controls. With tiny little labels that are impossible to read in dim lighting. I had to borrow a flashlight and use my magnifying glass to configure the monitor. The second one (an older model) has buttons. Yeah, I'll keep that one. What was Samsung thinking? Touch controls?! (And finicky ones, too.)

This may not be what causes it for you, but...
I've noticed something similar with my own flat-screen monitors, my wide-screen TV, and (this is the one that sounds weird) even the giant video scoreboard at Fenway Park. And, as you noticed, it varies with head tilt.
It's apparently my glasses, because I've also noticed that it goes away if I take them off. Sadly, I am so nearsighted that without my glasses I can't even read a computer monitor at normal distance.
Re: This may not be what causes it for you, but...