How much more valuable is a residential PV system when it is on a south facing roof (in the northern hemisphere)? Does it greatly improve the roi payback period?

Compared to east/west, or even southeast / southwest roofs? Are we talking 10% better, 20%, 30%?

it depends on the location: the closer are you to the equator - the bigger the difference. As a rule of thumb - deviation up to 20 degrees from South costs you under 10% loss in production. do your own math for roi.
As a software engineer you may entertain yourself by finding some simple free solar estimation tool to play with all the variables. good luck

Thanks Steve, thanks Anatoli! Played a bit with that tool, pretty cool. Wouldn't have found it without your help. If you hadn't guessed, I'm pretty new to the field so looking to learn a lot.