With that .570" ball, I would suggest 10oz. or 11oz. denim (Joanne's Fabrics). 10oz. denim will also work well with a .575" ball, which would be my preference.
A water based lube for target shooting, where the gun does not sit a long time loaded. Use an oil or grease-type lube for hunting, like Track's mink oil
or Neetsfoot Oil (the real stuff, not the synthetic) are the best for that use. Make sure you develop loads for a different lubricant, if switching lubes. Oft
times they do not shoot to the same point of impact.