The problem with using grey is that you need to overlight it to get a white background. I often do this with walls in our studio when the subject is 8-10 feet in front of the wall. With a sweep background this won't work. Since the subject is typically in the middle of the set, surrounded by/standing on the background there is no way to prevent overexposure of the subject when you overexpose the background.
The only choice is to paint with the color that you want... and repaint to change colors. In large studios they use 18" rollers and 5 gal. buckets of paint to make background color changes. They also charge the client for background color changes from and back to white. I don't know what the charge is but I wouldn't be surprised by a $500 charge for a large sweep. Part of this high cost is the number of coats of paint required to change colors completely. It can take 3-4 coats of white to cover a dark color completely. Eventually the paint gets so thick that heavy objects cut grooves in the paint which require spackling to fix. These studios usually have the floor scraped down to concrete every few years and start over.
What color of white to choose? I took a white WhiBal card (http://whibal.com/
) to the paint store and asked them to match it. They did an excellent match with their spectrometer. Now I just white balance on the wall and get great color balance. I also did this with the grey WhiBal card to get grey paint that covers most of the walls in our studio.