H4 - identity? Existance?

I've been working (bit by bit) on putting together a list of Proto-IE
roots taken from Adams and Mallory's "Encyclopedia of
Proto-Indo-European Culture". While doing this, the issue arose of the
use of "h4", a fourth laryngeal.

Now, I'm not sure if one can explain away all the cases where the
phoneme "a" is used. Even so, seeing "h4" over and over again got me
thinking. Here's what I came up with:

"DAMN IT, h4 CAN'T BE A GLOTTAL STOP OR IT'D VANISH EVEN EASIER THAN h1!

Perhaps, just perhaps, there was a uvular version of "k" (one might
call it "q") that was also used. Alternately, there was a sound midway
between "h" and "x" (i.e. h1 and h2). Or, quite possibly, there was a
"harsh h", which might well fit as h4. Consider that h1 (which became
an "e-schwa" and later lengthened Proto-IE "e") is lost in Hittite,
while h2 (which became an "a-schwa" and later changed Proto-IE "e"
into "a" or lengthened "a" [i.e. a:]) and occasionally h3 was written
in Hittite as "h" and likely pronounced like described above, and that
h4 is lost in Hittite but still managed to change Proto-IE "e" into
"a". This seems to suggest two possible features of h4.
Firstly, it is not as "strong" as h2; that h2 and h3 survived in
Hittite but h1 and h4 did not can attest to the fact that the latter
two are soft, easily unnoticed or omittable sounds. The possible
identities of h1 as "h", h2 as "x" and h3 as "yogh"^w seem to support
this: "h" is dropped very often in English, as it was in Latin, and as
it appears to have been in Proto-IE. The latter two are harsher and
more audible, and would not fade as easily. However, since it caused a
change in vowel sound (Proto-IE vowel to "a"), h4 definitely was not
as weak as h1.
Secondly, while not attested in Hittite, h4 does survive in another IE
language, Albanian. While admittedly Albanian is a bit bewildering in
its placement among the other Indo-European languages, it definitely
contains some archaic words, such as some borrowings from Etruscan.
That an otherwise unattested sounds also might survive in this unusual
tongue is not unlikely. There appear to be cases in which related
words in other IE languages use a vowel, Albanian uses "e" or – more
importantly – "he", such as in "herdhe", in comparison to Greek
"órchis", Hittite "arki-" and Proto-IE *h4órg^hiyeh{2/4}, all meaning
"testicle". However, since none of the other "laryngeals" are spoken
in Albanian, it seems likely that h4 is in a class somewhat apart from
the other three."

My guess (and this is only a guess) is that h4 is either a harsh
laryngeal fricative, or a velar "k" (q). But still, I'm not even sure
h4 exists!

I'd like to know - does this idea make sense? Are there other possible
identities for h4? Does h4 actually exist, and if not, where does the
"h" in Albanian come from?