I´m not sure about what was your question is, but flying under JAROPS means you are operating commercially.
Usually the aircraft on a AOC can be operated privately, but then before being commercial again, it would have to go through a maintenance check. Theoratically.
I know that some authorities grandfather some companies that can fly privately and commercially without doing that check...
In Europes Kuwait, you just put a P for private in the dutytimes-field of the techlog and thats it.