Sorry, looks like it was operator error! I misinterpreted the line I was looking at. I was focused on the bottom line "total requirement", which combines the actual SPAN risk parameter + "net option value" (the amount of cash I'd theoretically have if I was selling these deep ITM calls today). The SPAN risk parameter, the top line in the report, is actually correct in both synthetic and actual put cases.
Not completely operator error. The problem looks like how my FCM is calculating my risk margin. Because I'm primarily short volatility, the FCM is being conservative and forcing me to hold 200% of SPAN margin. I don't like it, but I'll deal with it. But the FCM's math is currently 200% of "total requirement", which includes all of the option premium that I sold. With a deep ITM call, the option premium that I "sold" is seen as being very, very high. If I switched to deep OTM puts, the option premium drops, and all of sudden my overall risk margin drops again. That can't be their intent...