Good suggestion about Tuples. I added a lazyTuples function on my development branch, though it's probably not in its final form yet.
I based the methodology of off the SE answer below. It's well worth a read if you ever want to work with large numbers of tuples:
https://mathematica.stackexchange.com/a/153609/43522
Edit
I think I did everything I for the implementation of lazyTuples right now. In the future I may try to implement a feature to generate tuples in chunks rather than 1-by-1, but the current code should already work quite well.
