This seems like a misconstrual to me. Anglican and Methodist orthodoxy still has prima scripturum, which is only a very nuanced difference to sola scripturum; both in theory reject influences that are incompatible with scripture as the principle authority.
> In the US evangelical and non-denominational Christian theologies generally posit that accepting Christ as your personal Savior (and the sole source of salvation) is all that is necessary to be saved (and Christian). //
This is not what sola sciptura is about. This is absolutely orthodox in all mainstream Christian denominations, that faith alone is necessary for salvation. Either group would consider the NT's exortations such as "what then shall we go on sinning?" (St.Paul) or "faith without works is dead" (James-the-Lesser) as primary teachings.
I'd actually consider that things are the reverse of your suggestion, that [USA/Western] evangelicals have strayed away from the Scriptures as a principle source of inspiration and instead rely on the characters of leaders and on self-help style influences that don't match well with the revelation of Jesus in the NT. Certainly it only takes 1hr of reading NT to find that being financially wealthy is contradictory to Christianity - not impossible to get to heaven and be rich, but er, maybe as hard as getting an obstinate camel through a tiny gate!?! Prosperity gospel, bah!
Could you highlight some of the characteristics that you consider go along with this.
"Deeply protestant" to me brings to mind the Quaker (a Protestant denomination) Cadbury & Fry chocolate companies. They did things like build municipal buildings, housing, schools. Fry family members addressed prison reform (Elizabeth Fry) and studied and acted to counter poverty and it's causes, for example. They reduced working hours too!
Sure, it was paternalistic, and they grew wealthy from their employees, but it seems they acted benevolently and genuinely tried to make a difference in their communities and for their workers.
https://medium.com/@cafonline/meet-the-philanthropists-sweet... gives a brief view.
What we hear of USA this side of the pond and these sorts of attributes don't seem to mesh.