I recently (last Friday) got contact lenses for the first time, after
21 years of wearing glasses, for myopia.

I'm a computer consultant, which largely involves programming, so I'm
in front of a monitor for hours every day.

One of the questions the optometrist asked was if I had dry eyes when
in front of the computer.  I said I didn't, quite truthfully.

Now, with the contacts, I find that they dry out pretty quickly while
looking at the monitor (a 22" CRT), necessitating frequent blinking.
The viewing distance is roughly 36".

While I can't be positive, it sure seems to me that the "drying power"
increases when the image on the screen is bright.  That is, with a
mostly black background, it's not bad, while a mostly white background
(or light grey, like the background I'm typing on right now) seems to
siphon the moisture out of my eyes.

I have no such problems when wearing glasses.  This leads me to
speculate that the monitor is throwing out a fair amount of IR
radiation, which is normally blocked reasonably well by the lenses of
a pair of glasses.  In fact, when I throw on an old pair of glasses
with the contacts still in, the drying effect certainly seems to
diminish noticeably.  Of course, it's a bit of a chore to focus with
an extra pair of diverging lenses (probably a good way to exercise
lazy eyes, though).

I don't notice any drying problems when looking at a LCD monitor at
much closer range.

Is my analysis of the situation more or less correct?

If so, would I be correct in guessing that something like safety
glasses (a zero-power clear lens) would help, by absorbing some of the
EM that's doing the drying?  Or would putting a flat piece of glass or
plexi-glass in front of the monitor (ignoring the mounting problem) be
an option as well?

Replacing the CRT with a LCD would seem to be an option as well, but
certainly the most expensive one.