The succeeding spot is defined as "where the ball would next be snapped.... had the foul not occurred". While your scenario did not give us the end result of the play, R apparently obtained the ball either at the end of the kick or the end of the run because they opted for the exception according to your post. Whatever yardline that was is the spot "where the ball would next be snapped ....if the foul had not occurred". But a foul did occur so R may now accept enforcement from that succeeding spot under the Exception to 10-4-2.
If I'm missing something, please tell me what it is.
You're missing the fact that if the foul had not occurred during the last play of the second quarter, the ball would next be put into play on the kickoff in the 3rd quarter. That's the definition of succeeding spot. It's been used that way since it was put into the rule book, until this exception, and now this debacle of a new rule change.
Read this again slowly:
Think about it like this: Suppose R doesn't want the penalty at all. They've had a good half, and just want to go to the locker room, so they decline the penalty. Where will the ball next be put into play? 3rd quarter kickoff, right? That's the succeeding spot. There will never be a situation where the ball would be put in play where it became dead at the end of the 2nd quarter if there is no foul, or the foul is declined.
This situation highlights the succeeding spot - the place where the ball would be put into play HAD THERE BEEN NO FOUL. If there had not been a foul, or the foul is declined, we would go to halftime once the play becomes dead, provided time runs out during the down.