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It seems that sspielman's suggestion (to calculate cooling impact of delivering preheated air to the zone directly) and then compensating it with a negative fictitious load eventually worked. "Eventually" because it also took quite a bit of tinkering with the OA controlller to understand why OA was a bit higher than calculated directly from the outdoor air design specification. I also had to add a bit of margin (~20%) to the fictitious load. Anyway, I got 0 unmet hours after 500 runs with semi-random occupant schedules. So I can move onward!

Thanks everyone for your help!