Has anyone found a way to dynamically populate a field on the invoice based on the number that it is in the sequence of a billing schedule? For example, if it was invoice #2 of 5 in the schedule, I'd like to display that on the customer's invoice PDF

That sounds like it would require a change to the advanced pdf template.

Ultimately, yes. But I'm asking does the data even exist to use on the pdf template? I can't figure out how to systematically calculate that this is invoice 2 of 5

You would probably need a script to populate the data on a transaction field first