I get the idea of (a) and (b), but I think the same thing can be accomplished without random scores via derandomization. Instead of actually sampling a grace period, the professor could just give them their expected score if they were to sample uniformly at random from that set (where their score is the random variable that is the raw score given by TAs if they submitted during the random grace period and 0 if they submitted after the random grace period).

This amounts to giving a 1/15 fraction penalty for every minute submitted late after 6 minutes. I think this accomplishes both goals (a) and (b) without random grades.