I like using the R authority here and going on the snap. Don't give them a timing advantage by fouling.
That's a "slippery slope," as they say in the TV lawyer shows. If it is a deliberate foul, then, yeah, they would get an unearned advantage. But, if it is a foul that is unintentional, and could happen at any other time in the game, then the opponent is not put at any greater disadvantage than they would have been at any other time, so the fouling team shouldn't be further penalized, just because it happened to occur near the end of a half. Certainly, holding fouls will probably be the most 'suspect' of live-ball fouls. Those are easy to commit intentionally while disguising them as unintentional. So, invoking 3-4-3 is supportable.
BBW, clipping, etc., are not likely to be intentional - not impossible, but not likely.
Thankfully, the Rules Committee took the judgment out of our hands when under 2 minutes in a half, for fouls by the team ahead in score. In the given example, one second later, we wouldn't be having this discussion.