I am in the 20th century where AD Eng 4/7 allows a C172 operating private on condition to be actually on line at a Flying School under an AOC , fact is the AOC nominates the type of aircraft on the AOC not specific registrations.
An ATO for example can operate outside an AOC and is within the regulations to test in a private aircraft.
Owners of Limited catgory aircraft almost always have the distinction of testing outside an AOC in privately owned aircraft, very few Limited Category aircraft operate under an AOC.
If the general view is to always lock your operation into the most restrictive regime imaginable the go for it don't let the enlightened folk be your guide, go for the most prescriptive method of operation you can concoct, CASA will love you, they really like overcompliant subservient operators.
Or simply obey the regulations as writ, nothing more, nothing less.