When the tech had the duct open, I noticed that the coil had a sticker on it
(model, serial number, max pressure) that said "Refrigerent:  R-22".

My system uses R-410a which I'm pretty certain is double the pressure of
R-22.  I asked the tech about this, and he said it probably shouldn't have
been installed, although two of his calls to a supervisor and another
employee seemed to indicate it was "OK" because either (A) it had a
regulator gizmo installed on it or (B) because that coil was "OK" for
R-410a.

I'm out of warranty by about 9 months and I may get this as a warranty issue
because the coil wasn't specifically labeled for R-410a use.  I understand
that coils usable with both R22 and R410a are commonly used now, but I want
to bet that they're actually designed that way from the get-go.  And that
mine was installed as way to avoid having to use a more expensive R-410a
coil, with a kludge to deal with the higher pressure.

Howard,

AC equipment is something I have a lot of dealings with and I have to
say that we only use unit with the matching gas. Whether or not a unit
is capable of using a different gas is down the individual
manufacturers build quality. The only way you can get the evidence is
by either finding out who made it and speaking to them or another
supplier who is willing to give advice on that model. I suggest if you
speak to the manufacturer to ask the basic Q first and not say where it
was installed and your supplier. They may not be willing to give the
info if it will cause a proble for one of thier suppliers or unit
manufacturer. I will say though it is the norm in business to cut costs
where ever possible and you may find that later models used a bigger
unit due to problems. Try and get some facts and whether you get them
or not try moaning on the phone lots. Often you can get something as a
compromise is better that the hassle and bad name.
Best of luck.