Re: PIE laringeals

There are lots of theories and no one really knows. My own views are
in constant flux. There does seem to be a widespread assumption that
h3 has a labial element but as you rightly point out labials and
labio-velars don't cause rounding. I think this very argument is
evidence against the existence of a labial element. All that is
necessary is that h3 cause the vowel to become more back. Unmarked
back vowels are rounded. Backing is therefore likely to be accompanied
by rounding. Also widespread is the assumption that h3 is voiced. I
don't think that is necessary for assimilatory voicing to be induced.
It should be noted that only the stops have phonemic voicing. If the
Glottalic Hypothesis is correct then the traditional unaspirated
voiced stops are really just voiceless glottalic stops. This suggests
that h3 need not be voiced but does cause glottalization. One
candidate for glottalization and backing of vowels is the glottal
stop. So far as I know cuniform does not have a symbol for the glottal
stop so the symbol for /x/ would have been the closest thing, which is
why Hittite would have used it.

For h2 I favor /h/ because it induces aspiration in stops in
Indo-Iranian.

I'm not convinced that h1 even exists. Putting that aside, my best
guess is /S/ but the evidence for that is mighty weak.