Oh my. I did that. It's tested and working as far as I can tell (my worst problem is not having a trustworthy source I can compare it to). But it's unpublished and in development. I will try to help out, but it's late here and I can't look at it now.
I have a complete project built and running - LED clock with RTC and Neo-6M GPS. There are some timing tricks that you have to pay attention to. The clock evaluates the GPS data and synchronizes the RTC time whenever the GPS is valid (and turns on an LED bar to indicate that). If GPS is lost, it ticks away happily on the RTC.
You may wonder, why would I want such a thing to be PPS accurate. Well, of course it doesn't, but I wanted it to be a base for future projects. Currently, the RTC PPS is only synchronized to the GPS PPS with about 30 microseconds delay (as I recall). So it's not all the way yet. But it's getting there.
Edit - okay, today I looked at your code. I see that you haven't begun to write any PPS code, so I can't really help much.