You are going in the right direction with what you are doing. The root system looked terrible in the old soil and photos, but looked better than I thought rinsed off.
You can water with RO or AC water, but AC water is distilled and will pull all the minerals and fertilizer out of your soil, so use it sparingly unless you are amending the water with fert and mineral supplements.
A lot of us use Hollytone or Osmocote (I actually prefer this these days), and it works great. You need to use very mild doses till your tree is growing well again and is full of leaves. If that is not available to you, I would recommend a very mild slow release fertiizer locally with a small dose of sulphur pellets. Again, if not available, aged chicken manure, and aged compost on top of the soil.