Kloekhorst has added
a new paper to his web site in which he argues in favour of *h2 having been [q] (uvular
stop) in Early PIE, and *h3 the same but labialized. His argumentation is basically that in Lycian, *h2 surfaces as a stop (transcribed
χ) posterior to the one transcribed as
k, and that the change
q > χ is common enough to have happened independently in Late PIE, Hittite and Luwian. Also, he points at some points where *h2 and *h3 behave like voiceless stops rather than continuants (e.g., by appearing as geminates in intervocalic position) in Hittite, and gives some other arguments as well.
It seems reasonably plausible to me, though I am in not really convinced by this (AFAIK, Lycian phonology is
very shaky ground, so using this language as sole evidence for such a reinterpretation of a PIE phoneme is quite a bold move); but what do you think about it?