regarding the alternative of a predominantly Irish or Pictish conquest, I wonder why that was not much of a thing ultimately, at least in places like Wales and Cornwall (for the Irish) and Northumbria (for the Picts).
Well, Gaelic influence in Britain was quite important historically : in Scotland, obviously, but as well in Wales (Dyfed seems to have been importantly gaelicized) or even beyond. The capacity of Irish missions to go deep enough around Irish Sea may have been related to Gaelic presence on both sides of it.
Lack of historical sources (and relative closeness you pointed out between insular peoples) makes it hard to fully appreciate their influence, but I think it shouldn't be underestimated.
Now what would be needed to make it obvious? Maybe a deeper differenciation between Brythonic and Gaelic people, preventing a quick fusion of populations (unchristianized Gaels, maybe?)
Eventually, Germanic presence may have been more organized since Roman times (as settling them on Saxon Shore, in more important and prosperous regions), and then maybe more inclusive of native elements (as in Wessex?)
Federated Scoti in Late Roman Britain may lead to a more important Gaelic "England" prosperity.
Of course, on the Picts, I have been starting to hear that possibly they may not have been either very distinctive or highly Gaelic, rather they were ethnically and linguistically pretty much the same people as pre-Romanized Brythons.
Well, we have too few informations about Picts to be certain of anything.
That said, I'd think Picts were enough distinct as a group of people in Early MA : Bede specifically mentions Pictish, Gaelic and Brythonic as different languages, after all.
That said, it could be the result of the "bastardisation" of a (already distinct?) "Northern Brythonic" trough contact with Gaelic speeches, as toponimy have a fair shere of likeness for what exist in Northern Britain.
Between the IVth and IXth centuries, you may had a fair deal of "creolisation", making it both distinct from Cymric and Gaelic alike, making it some sort of weird middle form between Q and P insular Celtic. Again, lack of important sources makes the solution uncertain.
Eventually, I'd lean to think that Gaels weren't outsiders for Picts, trough centuries of trade and political contact, making them (while distinct from Gaels) more inclined to be politically inclusive (that said, we know that Gaels of Dal Riata loathed Pictish kingship even when they submitted to it)