Welcome to the Fourm, SpillinaTech:
I would remove the duct insulation completely, spray the joists with a 25% bleach 75% water solution, scrape the heavy or difficult places and ventilate, ventilate, ventilate.
If the joists are damaged, they can be sistered with new ones; use screws rather than nails to install the new ones, to keep from disturbing the integrity of the present construction (causing squeaky floors).
Duct insulation comes in 4' wide 50' long rolls, is made of fiberglass with a foil backing that is reinforced. Cut pieces that will go around the duct and overlap 2". There is a special stapler that can be used to secure the insulation as you stretch it around the ducts.
I wish you the best as you take on this project.