So, when I replied here, did you go look at the program that does what you want? Did you have any questions?
That program logs complete NMEA sentences to an SD card, and does it very reliably. Since you're not really using lat/long to calculate something in the Arduino, you might as well avoid parsing it: just save the bytes you receive, don't waste time converting them to a floating-point number (or long int).
The Adafruit example usually works until you modify it. The "useInterrupt" feature will save one character from the input stream, once per millisecond. It's a way to avoid input buffer overflow. When an entire line has been saved, it gets parsed in loop. You say you don't need to do that, but that's what it does.
I have been asked about writing a "more modifiable" GPS logging example, as your kind of question comes up frequently. It's pretty far down my list of things to do, as my interest is really in parsing solutions, like NeoGPS. The link above is closest to what you want to do.
Cheers,
/dev