What makes you think Strathclyde would remain independent?
I don't think it would *remain* independent, but would be less tied with Scotland, and maybe more to England (even moreso if Anglo-Saxons takes back Lothian)
Mostly trough the political links between Dunkeld and Strathclyde, but apparently there's a arguments about these being the result of confusion between two persons. (Again, sorry, I've only limited sources at hand on this region)
If Dunkeld links with Strathclyde (Duncan and Malcolm III being king of Cumbrians with familial ties, as an apanage of sort) are exact, it could mean for the region to, while being still in the Scottish sphere of influence for a time, drifting away towards Anglo-Saxon Britain as it did in the early part of the XIth century already.
If these ties aren't historical, though...Strathclyde being more or less tied with Dunkeld trough Arpin familial ties, it's possible something
could play there as well, but less obviously so, if it does.
Would Dunkeld be able to hold on the principality, thanks to Northumbrian help, as a consolation prize? That's possible, but I'd think that the kings of Strathclyde would be still less "comfortable" with Moray/Fortriu Scotland, which could mean a more important focus on southern Scotland (and, subsequently, on them), making Dunkeld takeover of Strathclyde more or less useless. (What could be fun would be seeing them as "kings" of Lothian in the case of a partial reconquest, but I digress).
Do you not think that Mael would look to bring it into the fold through war or marriage?
That's possible, but another civil war (critically with Dunkeld being backed by Northumbrians) would have weakened a bit Moray/Fortriu possibilities, IMO.
Would clans be willing to undergo a war to strengthen formal suzerainity on behalf of a king that hold not only Moray but high-kingship?
After all, it would be the risk to undergo a defeat as Duncan's had against Northumbrians for Strathclyde with similar consequence after that Anglo-Saxons placed Malcom of Strathclye (which should be, then, differenciated from Malcom III of Scotland) back on charge.
It's more or less why I still think that Strathclyde would be more English-leaning in a first time : it could change, though, depending on Anglo-Saxons capacity to maintain their presence there.
Eventually, I think we'd need someone more knowledgable about Northern England and Scotland in the XIth century to be sure about it.