Very nice proposal, it's certainly good food for thought on the still uncertain history of how the different IE branches split from each other. As far as I've read about this topic, I think your tree should be much closer to the truth (which we will eventually find out, I hope so) than that made by some linguists, especially those who leaned toward the Anatolian Neolithic hypothesis for the dispersal of IE.
I must say, however, that to say that languages "evolve through population hybridisation" is only a half truth, because even in the absence of such genetic changes in the demographic makeup of the population there can be profound and unusually rapid linguistic evolution triggered by a random combination of societal and cultural developments (e.g. changes from Middle English to Modern English mainly between 1300 and 1650; profound phonetic changes in European Portuguese from 1600 to 1800).
Also, the mere isolation (not just geographic, but in some cases political and/or cultural) of two different strands of the very same people can lead to very divergent outcomes in the long term. So, I'd be a little wary of assigning all the development of independent IE branches to instances of population hybridization, though this interaction with absorbed non-IE peoples must have been one of the decisive factors in that history.
I agree with virtually all the proposed positions for the IE subfamilies in your tree, but I have two minor quibbles, which are the following.
First of all, it's important to say that these phylogenetic trees unfortunately have some kind of inherent flaw unless you establish some shaded connections between some groups that had originally started to diverge significantly, but apparently remained in closer contact with each other and ended up evolving/diverging more slowly than would've been the case, as well as sharing more areal features and regional dispersal of loanwords and new phonetic/syntactic trends (Sprachbund). There is also the very possible case that the language vis a vis Y-DNA makeup correlation became much more blurred and flawed with time because of the huge expansions of just a few languages (even in historic times, e.g. Latin, Gaulish/La Tène Celtic, but that also certainly happened in illiterate/unattested periods).
In my opinion, for instance, Goidelic (Q-Celtic) was probably not the original language of the R1b-L21 people in insular Northwestern Europe, because from a glottochronological perspective it simply does not look like it diverged soon enough from continental Celtic, including P-Celtic branches. Earlier, yes, certainly, but not before the final split of Celtic and Italic languages, related though as these latter may be. Most of the estimates I've seen place Q-Celtic Goidelic diverging around 800-1100 BC.
In any case, Goidelic is most definitely a sister to P-Celtic through an intermediate Proto-Celtic stage, and despite some superficial similarities (especially in phonology and basic grammar) P-Celtic (e.g. Gaulish) is not any closer to Italic than to Q-Celtic. There is also very substantial differentiation in lexicon between Celtic (Q or P Celtic) and Italic, which is suggestive of some significantly different (in geography and/or chronology) influences.
So, in my opinion the most probable scenario is that a para-Celtic tongue (more Celtic than Italic, but with affinities to both, maybe more or less like Lusitanian) had been the native language of the future Goidelic population, but they shifted to a similar but still distinct language during when huge "Celtic proper" (Late Urnfield/Early Hallstatt) expansion began - and of course they must've shifted to it in their own way, lending the new language much of the syntactic and some of the lexical peculiarities of their former language, this process being even made easier because the two languages were close enough to allow some hybridization without losing intelligibility (think of Portuñol Riverense in the border between Brazil and Uruguay).
So, to sum it up, for me the situation was a bit more complex: I'd place Goidelic as a very early offshoot of Proto-Celtic, probably due to language shift and linguistic convergence with an older sister language, and a bit further apart from them. Those early splits (Italo-Celtic into Celtic vs. Italic and then Goidelic vcs. P-Celtic vs. Italic) must've been really fast in historical terms, the probable sign of a rapid and huge cultural expansion (Urnfield?).
Beside that, I'd place Albanian (and probably its Illyrian mother or maybe grandmother tongue) together with Graeco-Armenian but in a position closer - and in some ways related to (maybe a dotted line could do that trick) - to the Northeastern branch, particularly Balto-Slavic. At least according to a quite comprehensive book about the history of Albanian vocabulary and grammar that I've read, Albanian shares the largest number of isoglosses first with Greek and second to Balto-Slavic, especially in fact Baltic languages.
So, in my opinion Albanian (and we know Illyrian came originally from further north in the Balkans, possibly near the ancient homeland of Balto-Slavic) should've been a sort of middle ground between the Southeastern/Balkanic and the Northeastern IE branches, subject to regional trends and share of loanwords (or maybe of similar non-IE substrate) not just with other Balkanic IE dialects, but also with Northeastern IE ones. The tree format doesn't lend itself very well to demonstrate these instances of languages that diverged significantly but due to geographic closeness, despite their distinct origins from different nodes, remain more closely related to each other than you would otherwise expect.
