Do you think it was a sort of convergent evolution or there's actually a traceable line of descent from this bit of Protestant theology to SJWs?

Yes, they weren't the only influence but they were an influential and founding one. All the seven sisters have on going involvement with Social Justice today.

I read it as, basically, refusal to consider the consequences

There is certainly a lot of that, especially among the more extreme radicals, which Pham's article is certainly part of. But the reason this can flourish in the discourse community is that it is being buttressed from the side by a sort of 'men of good will can always come to a reasonable agreement' article of faith. Even though Pham themself would reject this believe the fact that others in this community hold it enables Pham's disregard of feasibility. This is one big contribution that Mainline Christianity has been making to Social Justice, providing cohesion with this sort of ballast.

this value is deeper and more ancient ... As long at the cost is not high, sure, whatever makes you happy.

I would agree that this is an ancient value with regards to my family/my friends/my tribe , predicated on their continued acceptable behavior as members of the in group. But I'm doubtful about how far beyond that it would extend. In fact for those defiantly identified as out-group I would think it would be more "As long as the cost is not too high, whatever makes you miserable."

Christianity, as part of its universalizing, had a founding goal of drawing all peoples, languages, and tribes into one family group. Treating everyone as brothers and sisters meant having a care for their happiness.

I agree that SJWs don't seem very interested in making people happy (in fact I think this is one of those Moloch situations and everyone is actually producing unhappiness because of their incentives inside the situation) But SJWs do rely on general happiness goals in their audience. I do also think a lot of Social Justice thinking started out as a genuine desire to help people and make them happier, regardless of how that goal turned back on itself do to inconsistencies in other places in the philosophy.