Hi Elisiv Sounds like an exciting project.
I have grown using this method for 5 years now and have never measured the PH or nitrogen levels of my compost as I believe that the plants will seek out what they require in terms of nitrogen and that the PH only really matters to a very few plants such as blueberries (even they appear to grow quite well in a neutral soil).
Carrots and similar root very well through card as it disintegrates. Only thing I ever had trouble with was when growing icicle radish in a deep bag, they got so long they started pushing up out of the soil.