How plausible is it for the Romans in Britannia, alongside their Briton allies, to ride the tumultuous wave the WRE collapse and establish for themselves a stable kingdom?
Not impossible, but quite hard.
By "Romans" I assume you mean Britto-Romans, rather than either only military (that was anyway quite mixed itself, up to local and germanic recruitment). See, you didn't have real provincial identity in Roman Empire, and even the few you may have was even more weakened with the more personal and charismatic imperialship of the Late Empire.
With the decline and fall of this one in WRE, the basic identitarian structure was the pagi, the colonies and critically the tribes (either classified as cities or pagi themselves) whom presence never really disappeared.
This isn't just a British thing, it was the case for almost all WRE provinces :
Gaul,
Spain, Africa (constant overlapping of tribal and urban/peri-urban identities)...
The big exception being Italy, mostly because it passed directly from Imperial to Romano-Barbarian dominance.
In all these cases, the Barbarians that inherited the imperium and political legitimacy eventually were the unifiers of the dioceses. It's not about Britto-Roman or Roman population being too dumb to unify and to live, but about political and cultural trends of Late Roman era.
You'd probably need a PoD in late Republican Rome to deal with the relativly empty shell that were Provinces when it came to identity. At latest, you'd need something comparable to the
Sanctuary of Three Gauls, with its technically unifying yearly assembly. For the influence it had eventually on Gallo-Roman society in Late Antiquity, I'm not too sure it would be ennough to balance the aformentioned effects.
Eventually, if you want to bypass the provincial issue, you have to come back to the usual problem of Late Roman Brittania : isolated, not that deep romanisation (lack of many urban infrastructures, safe in an handful of cities; lack of rural infrastructures, with a low ratio of villae/latifundiae), demographically weakened (maybe 1 million after the epidemics).
Obviously, preventing the Roman army to leave for participating to the Scramble for Imperialship in 407 would probably help, would it be only because you'd prevent the mass expulsion of magistrates two year later. But that would ask for a complete re-writing of the era, giving that the withdrawal of Britain was a thing since the late IVth century : Britain wasn't nearly important enough compared to continental matters, and the withdrawal of 407 mainly concerned South and East (Irish raids encountering no real resistance in late IVth century).
It's why Saxon presence may have seen not so much as an invasion at first, but as well as possible allies
against the former.
not be a Roman successor state in Britain the way there was in Byzantine
Giving the cosmical gap when it comes to the revenues difference, it's pretty much a given.
but could the Roman elements on the island work alongside their native allies
You can't wholly separate "Romans" from natives after 500 years. Both eventually merged, would it be only partially.
Heck, even the Saxons (or an agglomerate of peoples adopting Saxon identity, trough Roman standardisation) present in Britain before the Vth century seems to have been fairly integrated trough military.
The big separation would be, for me, between urban Britto-Romans that may have looked a lot more like Gallo-Romans, and rural Britto-Romans that had really different references while still romanized (by this, understand creolisation of roman imperial and late celtic cultures).
Another rupture could be the South, more similar to the continental situation, and the North and West, that had a different and more distant roman influence.
to create one kingdom and keep any attempts by the Sea invaders from creating their own states in Britain from being successful?
The main problem there is you didn't have such thing as an "abandoned Roman Britain without ressources, that were only able to weep in their togas before the nasty Barbarians crushed them, saw Romans driven before them, and heard the lamentation of their women.
Saxons weren't exactly unknown in Britain, and at least present along the Channel coast, as in Gaul. You have a good chance for that Wessex line had either from Romano-Britain origins or that Barbarian fit in a previous situation there.