I've finally plowed through the supplements and the posts here and on Anthrogenica, and I agree as to the R1a-420 diversification in and around Iran and eastern Turkey. In fact, I think that conclusion could have been predicted even before this study; I think it's been clear for quite a while that both R1a and R1b have a connection to the area around the Caspian.
I also think, if you accept their sort of middle of the road mutation rate, which shows a date of around 4000 B.C.E. for the diversification of M-417, it looks like that and its downstream markers are very good candidates for yDNA lineages that were heavily involved with the spread of "Indo-European" culture.
Then, the question becomes
where did this diversification of M-417 and the creation of the "Indo-European" package take place. I don't think that this study provides any definitive answers. However, it's clear that the two main groups below M-417, roughly the Z282 "European" group and the Z93 "Asian" group are widely separated with very little overlap, as if, perhaps, two groups traveled to areas, perhaps niche areas, initially not densely populated, where their technological advances could make an impact.
I think archaeology should point us in the right direction. It has to be someplace where they adopted agriculture, as that would explain their sudden population expansion. It has to be somewhere on or near a "steppe like" environment given the proto-Indo-European lexicon. (This is a map I use for reference for the Eurasian steppe, although I don't know if it's the best one.
http://davidderrick.files.wordpress.com/2008/06/eurasian-steppe.gif ) It has to be someplace where they learned metallurgy, and adopted Kurgans.
I don't think the area adjacent to the Balkans makes the most sense given the modern distribution of M417 and particularly of Z93, and other reasons as well. (Much of that R1a is M458 and related markers and is from the much later Slavic expansions) Perhaps that area was initially more R1b?
The area just north of the Caucasus might fit the bill, but, depending on the theory one adopts, it could be either the primary or the secondary area of spread, or it could be the area of spread only for the so called "European" lineages.
Ancient DNA results will be of great help, but not just of the Yamna/Catacomb people, or even the Afanasievo/Andronovo people (did they carry different subclades of R1a?) but also of people to the east and southeast of the Caspian. Just finding out that the steppe groups in the Ukraine were M417 isn't going to resolve the issue in my opinion.
In terms of the archaeology, I'm a great admirer of Dr. Anthony and his book, but he is not the only word on the subject, although the English speaking world might think so, because they don't have the same kind of access to the work of people in other countries.
There is also, as just one example, Stanislav Grigoriev, whose works 'have' been translated into English.
https://islandvera.academia.edu/StanislavGrigoriev
In his on line book on the Indo-Europeans he provides
extensive archaeological support for a Near Eastern urheimat that is not quite identical to that of Gamkrelidze and Ivanov, although the analysis to some extent supports their work as well. (Part of the problem with any of these other theories gaining adherents, in my opinion, is that they are written in turgid 'academese', in comparison to the very well written and accessible work of David Anthony.)
https://www.academia.edu/3742220/Ancient_Indo-Europeans._Chelyabinsk_Rifei_2002_496_pp
Or there are papers like this one that posit that the Indo-European homeland might have been more mountainous than precisely "steppe" like.
http://jolr.ru/article.php?id=108
There is also Tservchkov's book from 2012, which I haven't read, but which Mallory claims supports the "Near Eastern" theory.
And even Mallory is honest enough to acknowledge that if there are problems with the other theories about the Indo-European urheimat, there are problems with the Pontic Caspian theory as well. It's only the internet 'authorities' who are so very...well...authoritarian about it, for a myriad of reasons...they, and those for whom this is a career breaker.
http://jolr.ru/article.php?id=112
On balance, I think there is much that makes sense about a "Near Eastern" urheimat, although it would require incorporating the ideas of several of these scholars, and especially, in my opinion, making sure to posit a 'secondary' homeland north of the Caucasus, However, the Pontic Caspian theory is probably, in my view, still more probable. I think making a final determination is just going to require more data.
It just isn't as clear as some people propose; if it were, all of these eminent specialists wouldn't still be in such disagreement.
Oh, this is the original Gamkrelidze and Ivanov paper.
http://rbedrosian.com/Classic/sciam1.htm
There are a few interesting short papers listed here that are unfortunately only written in Russian. If someone reads it and could give us a brief summary, that would be great...they say summary in English for some of them, but I can't seem to access it for some reason.
http://jolr.ru/publications.php?sort=issue&year=2013&issue=9