First point - the original post said nothing about a live-ball foul on either team. Why you muddied up the issue what that is beyond me, but OK, have your fun.
Second point - if the live-ball foul were on B, followed by a dead-ball foul on B, you would never have to worry about signaling the first down for B. Again, you're taking a very simple situation and making it very complicated.

And the cafeteria is featuring, crow served specifically for you and MCrowder.

Really? What in the world for? The OP made no mention whatsoever of this being a FED situation, and what I said is correct for the ruleset I work - NCAA rules. So ... why am I to eat crow?!?!

Can you provide a reference for NCAA that bears you out? If so, and you are correct, I will take my crow medium well with mushrooms and onions.

Why does Fed even bother to give a mechanic for something like this? Why not a general instruction to "present the facts in order of their occurrence and resolution", and let the official apply common sense? That is, recap in order. (They even do that in Rugby Union.)

If the first down is awarded last, it should be signaled last. If the first down is awarded and then penalty yardage applied after the line-to-gain is established, that's the order they should be signaled. A dead ball signal should be given in the order of occurrence of the dead ball, or first if the ball remained dead since the last administrative action.

Can anyone describe a situation in which this common sense rule would give ambiguous results, or in which a specified mechanic would make things clearer than this general procedure?

Robert