I am inch taller than you and I've had the same exact thought of doing quadrilaterals (no at the same time) to go up to 5'5/6 but the biggest thing holding me back is that my proportions would be noticeably out of place and also the long term effects. I've worn 2" shoe lifts and that itself makes my arm look kind of short in comparison to my body, if I did 2" more in my femurs it would be so obvious that something is wrong with my proportions. Imagine spending all that money on leg lengthening only to end up looking more weird. I would have to do arm lengthening in addition to LL. For me, with 2" more on my leg, my proportions are better so I would settle for that. I'm under no illusion that if I do quads + AL then that's going to come back and haunt me when I'm older.
I don't know what your proportions are like but I would strongly suggest you use shoe lifts and look at yourself in the mirror or take a picture/video to see how it looks and if adding more inches would make you look better or worse. You should pay attention to your proportions more than the numbers. Of course we all want more height but long term effects + proportions are more important, at least in my opinion.