I got a landing almost exactly 24 hours after local sunrise.

Well, the flight plan calls for a sun elevation angle of 10.8° and that would correspond to about 21 hours after local sunrise. How accurate do you need this? The moon rotates at an average of 0.516 degrees per hour.

I wonder if it's calculated into the simulators.

I'm not familiar with Starry Night (well, other than van Gogh's) and its capability. But most of those guys pride themselves on the weird, obscure stuff they accommodate. The software I used a while back was written by some guys who thought no computable factor was too insignificant.