You don't have to run Kawasaki or Toro oil as you stated due to the act, but they can suggest you use 20w50 before investigating any consumption issues under warranty since it is listed in the Kawasaki manual as a preferred option under certain environments.
With warranty claims it is all about documentation. If it were my machine and I was trying for a warranty claim, I would have the dealer do the oil change with Kawasaki 20w50 and Kawasaki filter, and have documentation for this change. Then I would keep track of how much 20w50 oil you need to add during the suggested service interval (usually 50-100 hours) and make a note of the date and number of hours since you had to add more oil. Once you reach the next service interval with this documentation if it is still consuming oil I would push for the warranty claim. This has been successful for a few of my customers with this issue.
With warranty claims it is all about documentation. If it were my machine and I was trying for a warranty claim, I would have the dealer do the oil change with Kawasaki 20w50 and Kawasaki filter, and have documentation for this change. Then I would keep track of how much 20w50 oil you need to add during the suggested service interval (usually 50-100 hours) and make a note of the date and number of hours since you had to add more oil. Once you reach the next service interval with this documentation if it is still consuming oil I would push for the warranty claim. This has been successful for a few of my customers with this issue.