Hello, everyone.
Oh, I haven't been lurking (much) - if I visit, I usually say something. I am not known for my reticence.

It's just that life in retirement, in beautiful (if somewhat rainy) Vancouver BC, has turned out to be busier in some ways than work in Geneva. I do many things, and visiting the Board has been relegated to the background. Also, I have just come back from a 3.5 week tour of Europe, visiting 6 countries, and I had little time for online activities during that time. (It would have been 7 countries, but Hungarian Railways advised me not to take the train through Prague, because the Prague-Berlin line was flooded out. So I flew EasyJet instead, Budapest-Berlin. I had to drop a visit to Prague once before - it seems God does not want me to visit the Czech Republic).
But now I have a question on Indo-European, I can't resist answering. In fact, I have a long-term plan to revise and greatly expand my pages on PIE. Hopefully I can do this before I die (just kidding).
On the issues at hand, my views have not changed much since the time I put them up on my pages in the first place:
1. On the velar vs. palatal series: I think that there is just one series, originally velar. This goes along with my belief that PIE, as far back as we can go, had a phoneme *a, separate from ablauting *e/*o/zero, and independent of *H2e > Ha. Original velars would have developed into palatals in many, but not all, environments in the dialects that later developed into the satem languages. One environment where velars were retained was before *a.
This is not the place to analyze all the data, but let me just give a quick overview of the situation of *k before (original) *a. On a quick count in Pokorny, there are 50 PIE etyma beginning with *ka- and 11 beginning with *k'a (palatal). Only 5 of these 11 have no alternate explanations: *k'ad- 'to fall', *k'ad- 'to shine', *k'a(n)k- 'to hang', *k'as- 'gray' and *k'at- 'to fight'. Maybe I can come up with a reasonable explanation of these forms, given my theory, maybe not. But I note that there are exceptions to palatalization rules affecting velars in Old English, for example (look up the history of "back" - why is it not **batch?). Dialect mixture? Analogy? Who knows - wait for my presentation when it appears.
2. On the question of labiovelar laryngeals, what surprises me is that no-one seems to have suggested this before me (if someone has, please let me know). If you look at Hittite glossaries, initial ku+vowel parallels initial hu+ vowel, both occurring with similar frequency. We know that Hittite ku+vowel corresponds to PIE *k^w, it is an obvious parallel to make a similar correspondence between Hittite hu+vowel and PIE *x^w (or *H2^w, if you prefer).
Here is a list of PIE words with *x^w, from my work in progress: *dl.x^wghós ‘long’, *g^wíx^wos ‘life’, *g^wix^wós ‘alive’, *x^wḗntos ‘wind’, *x^wés- ‘to dwell, to stay’,*néx^ws ‘boat’, *póx^wṛ ‘fire’, *sóx^wēl ‘sun’, *x^wl.'xnex ‘wool’.
And yes, indeed there is at least one case of *xw, distinct from *x^w : *píxwōn ‘fat’ [cf Gk pîar ‘fatty substance’] (I forget my reasoning, bear with me).
There is less evidence for the corresponding voiced labiovelar laryngeal, because internal H3 was lost even in Anatolian. But it is reasonable to reconstruct it at least for *g^woG^ws 'cow, cattle'.
I am firmly opposed to the phonetic identification of *H3 as *H^w. This is often done to explain the o-colouring of an adjacent *e. In my view this is contradicted by the fact that labiovelars are widely retained in Anatolian, Italic, Germanic and Greek, at the very least. Why would these branches have the uniform change *H^we > *Ho, when *k^we is retained in the same branches (with Grimm's law *k^we > *x^we in Germanic)?
I hope this gives a quick resumé of my ideas on the subject.