Slitherine

I like the new option to play on after a game completed through points. However, if the tide turns and the the defeated ends up as victor, is it the final score that is recorded, or the first?

That's kinda up to you - Bulge doesn't track aggregate win/loss record.

If I were playing and one person won, I'd consider it my victory, even if it were continued, regardless of final result -- but that's nothing official, just how I would feel.

The game tracks only one score. If you keep playing, the score at the end of the complete campaign is what is used to determine victory. Only you might remember the earlier jaws of victory.