[Dakota]

OK,simplifying the OP for discussion purposes.

S1 enters to bat unreported when B8 is due up. S1 hits the ball and reaches base.
B8 bats, hits the ball, reaches base and advances S1.
B9 bats, hits a double (this is to clear the bases of S1 and B8). S1 and B8 score.
B1 takes a pitch and the defense protests.

At the time S1 stepped into the batter's box, there is no confusion as to who she is batting for by rule (since she was unreported, we don't know who she THOUGHT she was batting for). She is batting for B8. There is no one else she could be batting for. The only legal place for B8, then, to re-enter the game is in the batter's box while S1 is still at-bat, or on base to run for S1. Anything else is illegal.

Do we agree with that so far?

Leave ASA out of the discussion. The OP was U-trip, and it has been stated that U-trip follows (by and large) NFHS rules. Since I have an NFHS rule book, but not a U-trip book, then I'll use NFHS.

I agree that NFHS (and by extension, U-trip) do not want cascading penalties, but they need to address this in the rules / interpretations. The problem is that once the illegal player completes her at bat, and then the other player's follow in order, to stop the cascade, we have to resort to some kind of made up interpretation. Not a bad solution on the field in a real game (especially if protests are not allowed), but this is a rules discussion board, not a real game.

Once we have B8 as an illegal re-entry, we then have the problem, again, of who she is re-entering for, and the cascade begins. There needs to be some kind of stop-loss rule here. Simple language about batters following in order or something would help. Or, even a "call it like we say, not like the rules say" official interpretation would work.

As I said, this is a situation that takes the unreported sub / illegal re-entry scenario beyond where the rules writers have apparently thought it though. It needs to be addressed officially.