In case anyone comes across this issue in the future, I figured out the problem. All of my glass defaults (windows, doors, skylights) were set to Glass Grey in the Transparent Glass materials options. For some reason grey glass does not transmit sunlight in my model (even though it says Transparent). Once I switched the glass to Glass Standard, I got the result I wanted. Very strange.
Here's an example with the glass door having grey glass, and everything else being standard.
Tupi22's post in Sunlight shadows not showing up in interior view was marked as the answer