I've been frought with stress this past week due to something ridiculous that happened to me. I'll recount my ordeal in the very next post coming up. At any rate, after deep relection, I think I have an awesome way to rework my theory to account for the uvular phonemes in Proto-Indo-European (PIE) much better than I had before and with the least amount of added complexity. As usual, you may want to consult my continually updated document Diachrony of Pre-IE to get a grasp of what I'm suggesting. Listen to this latest crazy idea of mine.
I would like to now propose that distinct uvular phonemes had already existed by the end of Old IE (OIE) when unstressed vowels merged phonetically to schwa. They were, as I stated before, initially produced by allophonic differences dependent on the neighbouring vowel. Originally at the Proto-Indo-Aegean stage (before 7000 BCE), a velar sound (ie. any of *x, *xʷ, *k, *kʷ, *g̰, *g̰ʷ, *g, or *gʷ) neighbouring the low vowel *a acquired an allophone with a [+low] quality (ie. *x → [χ], *xʷ → [χʷ], *k → [q], *kʷ → [qʷ], *g̰ → [ɢ̰], *g̰ʷ → [ɢ̰ʷ], *g → [ɢ], or *gʷ → [ɢʷ]). I've already mentioned that the Mongolic language, Khalkha, exhibits the same alternation. There are also the examples of Even and Yakut that are both undergoing similar processes of phonemicization of uvulars as I describe for earlier stages of Pre-IE. So when unstressed vowels merged in OIE, the nature of the uvularization automatically became obscured.
However to add to this idea, I also propose that Indo-Aegean's Decentralization of the inherited vowel system hadn't caused merger of former accented *ə to *a just yet. Rather, the two vowels must have remained distinct for a while in OIE until phonemicization of uvulars was complete.
With these revisions come some interesting changes to my views concerning some important roots and their prehistoric etymologies. For example, the well-known PIE root for "dog", *ḱwon-, might then ultimately originate from Proto-Steppe *kə-huni "tamed canine" (not *ka-huni, as I believed before), thus becoming Indo-Aegean *kəxʷanə and then MIE *kaχʷána due to Penultimate Accent Shift (PAS). The vowel *ə in that example, not being a low vowel, didn't uvularize the preceding word-initial velar stop to *q-, although the following laryngeal was uvularized by the second vowel. To explain another example, PIE *kreuh₂- "raw flesh", we must reconstruct MIE *qaréuxa- to account for it with a distinct uvular stop at the beginning to yield later PIE *k-. If this was a native term used in the earliest stages preceding PAS, then only *a may be prescribed in the first syllable in order to explain the later uvular, thus we should presume earlier *kárəuxə-.
This also has an impact on Proto-Semitic (PSem) loans that I identify in my online pdf. With the allowance of uvulars at this stage of cultural and linguistic contact between PIE and PSem, the interaction between the two will have to be revised slightly. For example, PSem participle *māšiʔu is now more understandably converted to MIE *mésɢ̰a- (> PIE *mesg- "to dip in water") with uvular stop *ɢ̰ because it would have been the closest approximation possible to a word-medial glottal stop for an MIE speaker. I maintain that word-medial glottal stops did not exist in the language at this stage.
I'll save my solutions concerning the possible geneses of the poorly reconstructed PIE particle *[ǵ/g](ʰ)[e/o] and the mystery verbal extension -g- for a later post.
 Fortescue, Language Relations Across Bering Strait (1998), p.72 (see link) explains that uvularization of velars neighbouring low and/or back vowels is quite linguistically natural.