I haven't updated this thread in a while. The H2O2 treatment appeared to work for about a week and a half but I started seeing little green threads appearing again. This time I set up a quarantine tank and caught all my shrimp and quarantined them in the quarantine tank for the duration of the AlgaeFix treatment which did work. I used 3 treatments as per the directions on the bottle, 3 days apart, just to make sure I got rid of it before I left for Christmas break. This looks to have worked so far but I will know for sure when I get back to my apartment on Friday. I've had someone caring for the aquarium while I've been gone.
Lesson learned: try Algaefix first. Much less labor intensive and I saw improvement withing the first 3 days and throughout the whole treatement there was do noticeable damage to any of the plants or the moss.