If we have Augustine style organisation move north quicker, with the increased power it gave the king over the church, we could see Pictland more adoptive of other AS church reforms...
But Augustine organisation was essentially tied to royal (or assimilated) power, from one part, and to the existence of a cities net to exist.
The power of monasteries above bishops is less a cultural one, than the presence (or absence) of these two factors.
In Merovingian Gaul, depsite the political dominance of Augistine organisation and the power of bishops trough both an exisiting and relativly strong urban net and royal support (as well both : merovingian administrative power being largely reliant on cities), you still had an important influence of Irish churches for monasteries (even if St Colomban rule was soon mixed with Benedictine during Carolingian period)
In "Scytmark" (yes, I like the name),the absence of a real urban net (I don't knwo much about Lowlands in MA, but basing myself on what Northern England looked like, I don't think it wasn't much more develloped) would be a severe obstacle to bishop power above monasteries.
Unless we have a royal power that already favours Augustine organisation (in all plausibility, an AS king), and manage by constant effort (aka, against the background tendency) to make them equally powerful facing lasting Irish-tied monasteries...
I don't think the solution to the OP request could be only a matter of religion, when we're talking of an era when religious organisation was tied to royal power and when said organisation was largely dependent of a defined background.
That of course might not be the convention at your institution.
Ah, maybe. I'm sorry for the confusion, then.
I always read "Irish Churches" or "Anglo-Saxon Churches" rather than Christianity (that is reseved for Latin, including Irish/Scottish, etc and Greek, not including Oriental churches).
Basically, Christianity is used for large ensemble, Churches for organised ensemble distinct from each other while they can be part of the same group, Liturgy and rites something else. (It's nowhere as formal in reality, of course)