I've been thinking about doing this too... Glad to see someone made the first plunge...
From my point of view using something that dries faster is NOT an advantage. The idea I would think is to get as much penetration as possible rather than coating the surface.
My idea was to make a big enough pot to soak the fabric in all at once. Even leave it soak for some time. My experience with dying was that it takes a fair bit of time for full wetting. So I figured the same here...
Then I was thinking of hanging it out on the clothesline to wipe down and let dry.
Also considered doing a very thin mix and multiple applications.