In strokeplay, only the scores (and stats) matter here. Any win when playing in a group does only count in the moment when it's displayed. Regarding the glitch that quitters will be declared "winner", it's positive.
More than your proposed extension, I'd like to see any challenge credit wins displayed, as, today, they don't count towards the cumulated earnings.
Edit: While I thought about it, these are private games, thus I'd not demand any display IRL.