Lunch Money: Pound of Flesh and Interactions

We recently had a game where a player got a POUND OF FLESH early in the game. Per the rules, all attacks are at -1.
This player was later able to GRAB another and put him in a CHOKE & PUKE stranglehold.
While the initial attack was Zero (1-1), we were perplexed with regard to damage for subsequent rounds. Thoughts?

We rationalized that damage to the victim was a direct result of the diminished-capacity choker, and therefore the damage would continue to be zero.

This story would be different, we deduced, if GRAB+COOTIES had been used:
While the first round of COOTIES damage would be zero, subsequent damage would be at full damage (One point). This is because it is the disease-- rather than the attacker-- that is inflicting damage.

What do you think? Does someone choking lose points because she's physically suffocating, or because the attacker is inflicting damage?

I would rule that "attacks reduced by 1 counter" means 1 less damage for each card subsequently played -- so if I have suffered Pound of Flesh and then I play Choke & Puke, the C&P does 0 damage immediately, but then 1 damage at the start of each subsequent round until the C&P is released or broken.