When switching dogs over, I've found grinding the meat and partially or even fully cooking at the beginning really helps. Also, go really slow, some pets have a hard time adjusting, others do the switch easily. Try a smaller butcher store (especially one that deals with wild game) rather than a meat cutter in a grocery store for grinding meat.
Roxy - Feb 2005 - 75 lb American Staffordshire Terrier (adopted Jul 2011)
Peewee - Jan 2006 - 8 lb Chihuahua (adopted May 2009)
Myka - Nov 1998 to Jan 2010 - 85 lb American Pit Bull Terrier cross
Lacy - Sept 1992 to July 2003 - 18 lb Reg Shetland Sheepdog