Stuck At Work Due To Weather

I'm a 12am-12pm plant operator for a local municipality. We had the ice storm this weekend and didn't get any guidance on how to handle it from supervisors, just knew I had to be there for my shifts (the plant must be staffed at all times). Other operators just said they were told to "be prepared to stay over", and that they'd been told to stay clocked in by ORC. Clocked out at noon per usual, went home and gathered some stuff for sleeping (they left a single dusty cot in the production area, and it had a brown recluse in it when I set it up). Spent some time with my wife and daughter.

Came back 6pm Saturday before the precipitation was supposed to start, clocked in, tossed and turned for a couple of hours trying to nap (all I had was a foam mattress topper, I slept on a table). Got up at 10pm and sat in the control room until my shift started. Worked midnight to noon as usual, got like 6 hours of sleep after my shift, did the same thing as the day before. Worked my last shift Monday till noon and went home.

Tuesday I got a call from my coworker saying our assistant director told people we won't be paid for "time spent sleeping." Wednesday he issued a retroactive memo saying "hours actually worked will be paid" but if you "elected to stay when other shifts were staffed" you won't be paid. Thursday, I got a copy of my timecard from my superintendent from the previous week. The AD had basically made up what times he thought I was actively working and ended up shorting me at least 2 hours. Marked all over it.

What pay am I entitled to here? I know the timecard deal is basically wage theft which I will address with him, but should I get paid for total time at the plant?

Location: NC