Played 3 more games: all of my opponents did not want (or know how) to play the new proposed rule.
Game 3: This opponent had not heard of the new rule proposal, so we decided to play as normal.
The rule would not have changed this game at all. My opponent never drew their SoG, and I didn't need to use NJ. FWIW, I did still use SoG in their territory to somewhat follow the new rule.
Game 4: My opponent preferred not to play the new rule because of lack of preparation (they were testing tourney decks and not wanting to playtest future rules). It turns out that the new rule would have changed the outcome of this game big time. Though I had my shot at winning (multiple shots in fact), the game still ended in a 4-4 tie because I am a noob.
I locked out their heroes and they locked out available lost souls. Had we played the proposed rule, I am confident I would have won (even with my mistakes). I'm pretty sure my opponent agreed with this assertion (I think they said as much if I remember right).
Game 5: We establish late if this game would play the proposed rule or not, so we decided to play as normal. Turns out, it wouldn't matter. My opponent's NJ was nailed by "deck discard" LS, and my opponent conceded before I was able to use my combo for the win. With that said, I would have a hard time using the combo because my opponent was not drawing a lot of lost souls (only 2 out of 33 cards). It was tough.