Make the kingdom of Strathclyde the foundation of a third kingdom between Scotland and England

[Andristan]

the East Anglian church was pretty definitively knocked out)

I would rather say that the Church in East Anglia wasnt knocked out, but was rather insignificant due to there not being a important bishopric located in the territory, unlike in York or Lincoln where the local bishop was a much bigger deal.
In my little scenario above, the Bishop of Govan/Glasgow/ Royal Bishop of Strathclyde is likely to struggle with both York and Canterbury, possibly St Andrews for independence, if St Mungo's See remains the chief see of the kingdom then I can see it getting recognized as independent around 11th or 12th centuries. Now that I think about it, York might not get elevated to the archbishopric status, especially if Strathclyde controls Carlisle, Mann, and Whithorn, unless Viking York stays around connected to the Five(four) Buroughs then it would be a more Southumbrian ecclesial territory.

 

[cincpac overboard]

the Bishop of Govan/Glasgow/ Royal Bishop of Strathclyde is likely to struggle with both York and Canterbury, possibly St Andrews for independence, if St Mungo's See remains the chief see of the kingdom then I can see it getting recognized as independent around 11th or 12th centuries.

Politically, how does an independent bishopric help the kingdom of Strathclyde? Does it have an economic benefit as well, such as say increased pilgrim flows through the kingdom?

 

[Zireael]

Politically, how does an independent bishopric help the kingdom of Strathclyde? Does it have an economic benefit as well, such as say increased pilgrim flows through the kingdom?

In this time period, having an independent bishop gave you a lot of clout and importance. See how Mieszko fought for Gniezno to be recognized as a separate bishopric

 

[Andristan]

In this time period, having an independent bishop gave you a lot of clout and importance

Exactly! Being not subordinated to anyone but the Pope gives a lot of prestige which increases regional significance, it does have some economic importance as well, Govan would not have to send part of its tithe to a superior bishop, though later on in the medieval period it would be subject to the Peter's pence, sending some of its collection to Rome. Govan being independent of Canterbury might allow for a bigger promotion of St Kentigern, its supposed founder which would increase pilgrim visits and thus have another economic impact. Politically, it allows the king more freedom in pushing his candidate into the position, though it also increases the power of the bishop and that could be a problem if they do not see eye to eye on an issue. It allows for the growth of the medieval healthcare and guesthouse system which was based on monasteries and churchs so might see a bigger population, though it could lead to less taxable income as well.

 

[Hastings]

Also at least in the British context it was tied closely with sovereignty. Both the Welsh and Scots wanted their own separate Archbishopric though only the latter succeeded. The English thought they should be subordinate religiously. And coincidentally also politically.

 

[cincpac overboard]

With an independent bishopric might the church in Strathclyde be able to engage in cathedral building/expansion? What kind of social and economic services can a cathedral provide that a smaller church could not? Perhaps we start seeing Bibles in the Cumbric language, aiding the spread and standardization of the language, at least among the clergy in Cumbria?

 

[Analytical Engine]

Perhaps we start seeing Bibles in the Cumbric language, aiding the spread and standardization of the language, at least among the clergy in Cumbria?

That's unlikely until later on.

However, it is possible that Cumbric monks may create a standard script for the language, similar to what happened in Ireland.

 

[Andristan]

We could see, if the kingdom persists, actual written documents in Cumbric, we can be pretty sure they existed due to comparison with both the Scots and the Welsh principalities, something like the Welsh chronicles though those were in latin, like most written works. We might even have more of the old bardic poetry in the vein of the Gododdin, seeing as most of the supposed old bards were from the Old North.