if you do a search though my posts, you'll quite a few relate to the very process you are asking for.
As for the water. It depends you can run a solution through but you need to pick something either on the acidic side of the scale or on the neutral side. if you run a full scale cleaner through you will likely leave the fiber to alkaline, along with not rinsing out the remaining detergent. that will re attract dirt.
if it was me...
I would find a good preconditioner for cold water cleaning (this means heated water extractors under 150*F) I would, after i have prevacced the fiber, apply the pre conditioner via spritzer bottle. Lightly work in with a brush to besure the detergent is coat as much fiber as possible. then i would have a rinsing agent in my solution tank. An all fiber rinse, or a slurry. both will bring the ph of the fiber close to 7. After that i would drop air movers to dry the fiber as fast as possible.