First off, hugs honey. Motherhood is NOT easy. And anyone who tells you it is, is lying!
Definitely cannot advise you on GF as that is not our program. So, I'm afraid you'll have to pursue that on your own.
But I can tell you my concerns: 2 45 min cat naps plus a 2 hour nap is only 3.5 hours of daytime sleep. At this age, most LOs require more like 4.5-5. That routine might work OK at first, but for many children (especially touchies) they will start to get cumulatively OT which will either give you NWs and/or EWs. I just don't think it's a long term solution.
That said, there is absolutely no reason why some days you can't just chuck the whole A time thing and get out and enjoy the day! LOL! As long as you tell yourself "We are not worrying about naps today. if she takes a great nap or two, fine. If not, then who cares because we're going to have fun."
Also, this is SOOOOOOOOOO temporary!!!!! You are on the CUSP of the 3 hour A time window at which point life really really REALLY opens up! With 3 hours it's so much easier to get out and do stuff without the risk of them falling asleep in the car. In another month she won't even have a cat nap which also gives you more freedom. I know right now it feels like you've been counting As forever, and that you will for another stretch of forever. But the first 6 months are so hard!!!! The 2nd 6 months get progressively easier. A year from now, it will be a whole different universe, and this first year will be a blur.
It's all about finding a balance between what works for your child and what works for your family. If you've just had it with counting As, take a day or two off and with my blessing!
Everyone feels that way sometimes!!!
Now, for the schizophrenic A times, LOL! I really suspect she's got teeth on the move. When that happens, they are exhausted one day and need a shorter A and then the next day they are totally wired and ready for more! 1h15 *does* sound UT to me, and you were doing more like 2h40 before. You might go back to that and see how she does.
Personally, as long as she sleeps an hour I wouldn't worry about it too much. She's going thru some kind of something right now (I think it's teeth) and so it's better for you to just pick an A time and stick with it for awhile and keep your sanity. If she sleeps more than an hour, great. If less than an hour then we know we have to pick a different A to stick with.
Obviously the car nap was messed up. This is also an age where even if kids were movable before, they aren't now. You were lucky to get it to last this long. My touchy little guy NEVER handled being moved. Not even at 3 weeks old.
Hang in there, love! You can pick whatever method you want, but I can tell you truthfully that a method only works if you stick with it. If you need to take a break from sleep training, do it. I'll tell you another little secret: some kids are just touchy about sleep. So, even if you decide to wing it for awhile, it may not mean more peace for you at home b/c your kiddo will be so exhausted. I wish we could all get easy kids who do fine even on little or no sleep. But it doesn't work that way. Some kids are just harder to figure out in the sleep department, which is why BW was invented!
I had a touchy guy, and my DH was about to clobber me over the head with a frying pan if I said "Overtired" one more time in the first couple of years of his life. But we made it thru, with some phases being easier than others.
Do what you have to for your sanity's sake. But don't feel like you're alone. We alllllll been there. And eventually they do get bigger and have fewer naps, and life gets easier.