You need to fail one of the test parameters. be it oil usage, compression, leak down test etc. Oil usage you can check, must be if using that much oil. Works out to about 60 gallons of gas you are burning a quart of oil. The other tests you could do as they will charge you to do, unless its Mill coding.
We went through this with our 3.6 in the 2012. to warranty the motor it needed to fail a leak down test. It had Mill coded as well. Result was leakage of two exhaust valves in each of #2 and#6 @ 75% and i think a pass(OK) was like 18% or more. New head was put on. well known issue today effects many 2011-2013. we carry spar heads you just need a case of oil
3.8 oil issue is somewhat well known. more than a few treads on this.