It will take a bit of time, but I would continue with the cardboard form system you have in place. You don't say how wide the fabric is, so I'm going to assume that it is around 42" wide. Unfold the entire piece, then fold in half length wise, then in half again and wrap around the card. I think you are planning on cutting the yardage into small squares (?) there's really no reason to keep it in the whole uncut length. So if it's too cumbersome to wrap the whole 6 yards, cut it into 2 3-yard pieces.