I don't have time to fully annotate my sources in this post, but I think a synthesis of the Bell Beaker and Basque narratives is possible at this point (even in advance of a huge dump of new ancient DNA evidence in a couple of months). In a nutshell:
1. Early Neolithic (ca. 4000 BCE-3000 BCE).
Iberia is at the far fringe of the Neolithic and the earliest Neolithic in Iberia does not receive the full Fertile Crescent package. In particular, they get cows at a latter date in some places. different waves of the first farmer Neolithic reach different parts of Iberia. In the east the Cardial Pottery Neolithic is the first wave. Elsewhere, a different Neolithic wave if the first to arrive. Also, there is a substantial fishing subsistence culture in the Mesolithic in parts of Iberia and this kind of subsistence has greater staying power relative to Neolithic cultures compared to terrestrial hunter-gatherers.
The bottom line of all of this is that Iberia's first farmers are less dominant than in some places and therefore integrate more Iberian hunter-gatherers into their first farmer communities than many places in Europe.
mtDNA H1 and H3, HV, and V are probably all Mesolithic in Iberia with a source either from a Mesolithic migration from the East or from a Franco-Cantabrian refugium that expands south into Northwest Africa and North as far, eventually, as the Arctic Circle on a more or less coastal route each way for the most part.
The Neolithic Y-DNA would be a mix of mostly I2 and G2, and the autosomal contribution from the Neolithic which would be the strong majority (but not quite as strongly as in other first farmers) would be Sardinian-like.
2. Proto-Bell Beaker (ca. 3000 BCE- 2800 BCE).
Proto-Bell Beaker people are drawn to Iberia primarily because of its metal resources in a gold rush like migration, and because it doesn't have an established full fledged Copper Age/early Bronze Age technological package.
The Proto-Bell Beaker migration is male dominated and made up of men with Y-DNA R1b-M269 or closely related clades, who have some steppe ancestry. These Copper Age/early Bronze Age men are skilled in metal extraction and metal working, cattle herding, archery, and maritime travel. They aren't necessarily all that expert as horsemen.
Some of the minority of women in the migration were probably mtDNA U5a and the women have a below average proportion are mtDNA H. But, they end up making a modest share of all maternal ancestors of the Bell Beaker people by the time that ethnogenesis is complete and expansion has begun in earnest at least among the expanding/migrating populations.
This may have been a stream of migration that lasted for several generations, or could have been a coherent migration of a small number of related clans.
I am agnostic at this point over whether it is a maritime migration or an overland migration.
The rise of cattle farming and the distribution of R1b-M269 related clades favors an overland route. But, the evidence of their maritime skills and the long distance traversed, much of which was occupied by technological near peer Indo-Europeans of the Corded Ware branch favors a maritime branch. Potential sources for this population include the Southern European Steppe (more or less the Yamnaya culture), Southern Caucasus, Anatolia, and Crete. They could have been proto-Indo-Europeans but more likely were not.
3. Bell Beaker Ethnogenesis (Probably In Iberia ca. 2900 BCE)
Upon arriving in Southern Iberia, the Proto-Bell Beaker people move into leading positions in existing communities with immense cultural and religious impact and marry local women in multiple successive generations, leading to a cultural transformation and ethnogenesis of this admixed people dominated by the proto-Bell Beaker culture in many respects that becomes the true Bell Beaker culture and expands from there.
Maternal genetics are predominantly Neolithic and pre-Neolithic.
Paternal genetics swiftly become R1b-M269 dominated because the patriarchal Bell Beaker culture gives a huge advantage to the technologically more advanced proto-Bell Beaker men over local men.
The autosomal genetics becomes quite Neolithic relative to the proto-Bell Beaker people because of multiple generations of dilution with local women (must as is the case in Latin America and in Chadic people), but less extremely.
The proto-Bell Beaker people may be the source of lactose tolerance genes, Rh blood type genes, and other distinctive Basque-like genetic traits. About 95% or so of steppe ancestry in modern Basques is due to these men and a similar percentage of steppe ancestry to that found in the Basque all across former Bell Beaker territory is also of Bell Beaker origin. Any additional steppe ancestry in people in this their former territory (maybe 5%-15%) comes from Celtic and Germanic Indo-European migrants.
The linguistic aspect of this is not clear.
One possibility is that the proto-Bell Beaker men adopt the Neolithic language of their formative area shared by their wives (probably derived from an Anatolian language of ca. 6000 BCE and split into a big LBK v. CP Neolithic subfamily and from their into local dialects), possibly with some grammatical (and almost certainly some lexical) influence from the proto-Bell Beakeer language (which could have been either early Indo-European or non-Indo-European with possible links to Hurrian, Caucasian or Minoans).
This happened in the case of Roman conquerers in the Eastern Roman Empire who came to speak Greek, to Norse conquerers in Russia who came to speak Russian, and to the proto-Chadic R1b-V88 who developed a language derived from Cushitic with other influences.
Another possibility is that the local Iberian population in the Bell Beaker areas adopted the proto-Bell Beaker language subject to substrate influences (in this scenario the proto-Bell Beaker language was not Indo-European and was ergative). This happened in most cases of Indo-European expansion, in Uralic expansion, in Hungarian expansion, and in the Yayoi invasion of Japan. On balance, I think this is more likely, but either possibility could be consistent with the facts.
Either way, there was some influence from proto-Bell Beaker in lexicon that lead to some basal Indo-European terms being either borrowed by the proto-Bell Beaker languages nearby or part of the proto-Bell Beaker language absorbed by the surviving local Neolithic Iberian language.
Either way, the end result of this ethnogenesis and language event is that post-ethnogenesis, the Bell Beaker people speak the non-Indo-European proto-Vasconic language.
4. Bell Beaker Expansion (mostly Bronze Age)
From Iberia, the expansion of the newly formed Bell Beaker people is rapid because it is filling a vacuum caused by a first wave Neolithic slump that set back the first farmers and because of their superior technology. This expansion takes place up river basins, overland and by sea. It went to France, Sardinia, coastal Northwest Africa, the Canary Islands, Belgium, the Netherlands, the British Isles, Ireland, Denmark and Iceland. There is a fair amount of trade and interaction within the Bell Beaker sphere. This expansion may have more men than women, but is not nearly so male dominated as proto-Bell Beaker.
Their culture makes pretty strong social divisions between Bell Beaker caste people and local people with the Bell Beaker people receiving superior treatment and leadership roles disproportionately.
This and Bell Beaker male social dominance leads to a dramatic expansion of R1b-M269 and related clades and dramatic expansion of mtDNA H from their wives in Western Europe.
The Bell Beaker culture becomes differentiated from a common source as it expands, but trade ties and shared cultures remain. The leadership, in particular, remains fairly mobile.
The expansion is also the source of the Vasconic substrate in European toponyms and a shared substrate in Celtic languages.
5. Narrow Basque Ethnogenesis (later Bronze Age)
One branch of the Bell Beaker expansion reaches France, possibly enriched in Northwest Europe with lactose tolerance genes if they were novel mutations in this time frame rather than brought with the proto-Bell Beakers from the Steppe or West Asia.
One differentiated subgroup of these Bell Beaker derived people back migrate to the South and end up in modern Basque Country, probably ca. 2600 BCE to 2400 BCE, and give rise to the modern Basque people with their derived dialect providing the sole surviving language of the Vasconic language family of the Bell Beaker people when the others go extinct in the next phase, even though it isn't terribly basal within the language family and is far removed from any proto-Bell Beaker language.
6. Bronze Age Collapse (ca. 1300 BCE to 800 BCE).
After a thousands years of a standoff between Bell Beaker derived people who speak a non-Indo-European Vasconic language and Indo-European Corded Ware people with comparable but different technological and cultural packages that roughly leaves Western Europe and the Baltic Coast to the Bell Beaker derived cultures and the east to Corded Ware derived cultures, the climate events that give rise to Bronze Age collapse happen and the Bell Beaker culture collapses while the Indo-European Celts in the South and Germanic folks in the North surge into former Bell Beaker territory leading to language shift everywhere but Basque Country eventually. These people are the source of the additional steppe ancestry and Y-DNA R1a in Western Europe.
The similarities of Celtic languages may, in part, be due to similarities of both the Indo-European superstrate which was probably originally more like Italic, and similarities in the non-Indo-European substrate which was broadly Vasconic but had diverged into regional dialects that probably more or less match the Celtic linguistic subfamilies.