3-3-4 would apply because we won’t replay a down when a safety is involved, right?
That is oversimplifying the rule a little bit, and is complicated by the new tack on rule, which is the absurdity that we're all pointing out in this thread.
Beagle's First Situation -- During a scrimmage kick down during which time expires, K commits a foul in their own end zone. Result of the play is a safety.
Previous years -- R has the following options: a) Decline the foul and take the results of the play (a safety). Period ends since there is no accepted foul. b) Accept the foul, the enforcement of which is a safety due to the enforcement spot being ABO, in K's end zone. The period is not extended due to 3-3-4.
This year -- R has an additional option: c) Accept the results of the play and enforce the penalty from the succeeding spot. In this situation, the result of the play is also a safety BUT the safety was not a result of the enforcement of the foul (3-3-4(b)5: "... the penalty is accepted for fouls for which enforcement, by rule, result in a safety"). By rule, the succeeding spot enforcement of the foul is not the safety. Since this enforcement option does not trigger 3-3-4, the period must be extended to allow for a succeeding spot for enforcement purposes.
Beagle's Second Situation -- During a scrimmage kick down during which time expires, K commits a foul simultaneous with the snap. Result of the play is a safety.
In this situation, the only thing that is different is Option B. Accepting the foul with basic spot enforcement has the enforcement from the previous spot, which does not result in a safety, so now 3-3-4 is not triggered and the period would be extended. Situations A and C are still in play and the same outcome as previous.
The simplification of "We don't extend when a safety is involved" held previously because when a safety was involved previously it was either a) the result of the play (and you'd have to decline the foul in this situation) or b) the result of penalty enforcement (which always triggered 3-3-4), but that simplification falls apart because there is now a third option on scrimmage kick downs with succeeding spot enforcement.