The late steppe (Poltavka, Sintashta, Andronovo etc.) was profoundly influenced and probably linguistically and culturally changed by R1a males bringing in a much more CWC-like admixture differentiating the MLBA population from the EBA. That is why I think that Indo-Iranian, yes, did originate in the steppe, but via a mix of local steppe with a back-migration of EBA Steppe + EEF people from the CWC horizon.
If I understood your hypothesis correctly, the spread of IE languages by R1b-L51 men was associated with the expansion of BBC and concomitant retraction of R1a CWC haplogroups, with non-IE L51 BB males shifting their language to that of their CWC women. If the process of formation of the Northwestern IE languages were like that, its birth would be roughly in the end of the CWC and its replacement by BB in Central/Central-Western Europe, wouldn't it? By that time the centum vs. satem proper divide would've already happened (I'm not including here other satem-like developments that happened later in other IE branches, but which were not "the" satem sound changes per se), and, if CWC is somehow associated with Balto-Slavic and Indo-Iranian as many people believe (which would explain nicely the clear Indo-Iranian influence in Proto-Uralic and Proto-Finno-Ugric especially), then it's probable that the languages of CWC would've been satem and a centum Northwestern IE with many pretty "archaic" features, in comparison with Balto-Slavic and Indo-Iranian, couldn't have been born out of such CWC IE branch.
AFAIK the Vasconic Substratum hypothesis didn't have any level of relevant support among the broader community of linguists. It wasn't well received at all. What are the influences of Basque on Q-Celtic that P-Celtic lacks? I have heard about a supposed (and also widely rejected) Afro-Asiatic(-like) influence on Goidelic Q-Celtic, but not about Basque influence (not apart from very tenuous things that are not demonstrably "Basque" in origin, like the vigesimal system also found in other parts of Europe that were not part of the Atlantic Bronze Age). The non-IE substrate is also apparently too small to have such a significant and unquestionable presence as it has for example in Greek and in Anatolian. If R1b-L21 Ireland had adopted Celtic directly from U152 Celts, having spoken non-IE languages before, and not being subsequently replaced at all by the incoming people (not even the males), I think we could at least expect for a larger non-IE substrate.
Another thing that makes me wary of ths "non-IE Britain until the Iron Age" hypothesis is that the pre-Celtic population apparently already carried a very steppe-enriched genetic structure to the British Isles, after all the big genetic replacement happened in the islands in the Early Bronze Age, not when the Celtic language "proper" (derived from Halstatt) arrived there in the Iron Age. When they came they already met a very autosomally Celtic-like population there. I find it unlikely that that population (including L51 males) would've come straight from Iberia and without steppe linguistic and cultural heritage.
Firstly, check out my immediately prev. post for my updated theory - basically, U106+Corded = Germanic, U152+Hungarian Yamnaya = Italo-Celtic (I am completely set on this and will never change my mind unless aDNA contradicts it, it just fits so massively well).
About your point with Corded Ware - I'm of the opinion Corded Ware left the Steppe before satemisation occurred, and that Balto-Slavic and Indo-Iranian are derived from other R1a folk that left the Steppe after satemisation took place.
And about the Vasconic substratum hypothesis - most linguists don't believe it in its extreme form (which I think is as crazy as after the LGM, Vasconic speakers spread out from the SW and covered at least a huge chunk of Europe), but the
Goidelic substratum hypothesis is pretty well regarded, and the leading candidate for the substraum iirc is Vasconic. EDIT: Actually, I'm not too sure about this - all I know is that a non-IE substratum amongst Goidelic is a widely held view. The P/Q split isn't very important, though, as it happened in Italic too, which suggests that (and this bit isn't just me talking, but linguists) the change was bound to happen at some point somewhere, and the Q regions were more conservative (with both Italic and Celtic, the Qs were the ones who seem to have departed first (the Insular Celts and the Latino-Faliscans - the Britons being P can be explained by more recent contact with Gauls, as is known to be the case)).
With the Steppe-enriched Brits (which I am pretty confident isn't over 50% as is suggested, as it so is not fair to just assume all EHG+CHG is of Steppe origin - take the example of Sicilians for example, who have plenty of CHG not of Steppe origin (and in my L51 theory, with it coming from the Middle East, you would
expect CHG)), I put that down in good part to the aforementioned point about e.g. the CHG, but also to the fact that there would be some low amount of EHG anyway given in my theory M269 expanded from the Balkans into West Asia to form L23 (sailing to Iberia to form L51), and this M269 I am presuming to be similar to the Iron Gates HGs (so for simplicity's sake, some combination of WHG and EHG).
Any remainder of the Steppe that cannot be accounted for through assuming existing CHG and EHG before the L21 contact with IE would be put down to mixing with the Corded folk (BUT more "touch and go" than residing amongst a whole bunch of them - not very scientific I know, but it makes sense, just as Frenchmen in the Southwest have more Spanish influence despite retaining the French language). This can be seen in the fact that with the Rheinish Beaker and British Beaker (of Rheinish origin ultimately) crania analysed by Coon, there was a combination of Corded type very strong dolichocephals (accounting for about 25%, and about 10 points lower in terms of cranial index, which is bloody huge and basically confirms they are distinct from the rest of the samples) and Beaker type brachycephals (accounting for the rest, ignoring the contribution from the original Borreby population) - the Corded type makes a decent impression, but it isn't the majority as would presumably be needed for it to be plausible for adoption of the language these Corded folk spoke. If you were to try and average out the CIs, it would roughly approximate modern Celtic CIs (a mesocephalic index). HOWEVER, the IE folk from later periods (for example the Unetice folk) were very dolichocephalic (usually, only marginally higher CIs than Corded Ware folk), suggesting a far greater Corded influence - consistent with the Corded folk making up a large chunk of the population, and so making the language adoption theory feasible in that particular case. This should be obvious, though - the Corded folk, deep into their territory, didn't just disappear, even if the males were wiped out. They simply became part of a new culture.