Bonny,
Excepting tapered cross pin takedown systems, I suspect nearly all are subject to wear and loosening over time. The original BSA tapered cross pin in my opinion is exceptional (also used on Fraser takedowns???) in that it both indexes the barrel to top dead center as it 'lifts' the barrel up and creates a firm lock between the barrel and action.
The keys to reducing the likelihood of Morris' system for this project (and his two-barreled set) failing over time is the care and fitting that he gave the barrel to the action. The proper 55 degree Whitworth threads were cut and lightly chased with a small triangular file to remove any roughness so that to begin with the barrel had a snug fit in the action. I suspect most Martini actions that are rebarreled short cut the Whitworth thread with 60 degree threads.
Secondly, Morris cuts his barrel threads right up to the face of the barrel tenon. Thus the actual contact surfaces of threads is maximized. His thread cutting tool is an interrupted 'V', that is one leg is shorter to allow a very close cut to the face. An image from the other Martini thread is attached to emphasize how close the threads get to the face. It is mesmerizing to watch him thread a barrel. His coordination of stopping the feed and withdrawing the cutter at precisely the right moment is amazing.
The third key is to work the barrel and action threads many times bringing the barrel into full contact each time with the action face thus 'wearing down' most of the high contact points on the threads. This ensures that thread to thread contact is significant. Once this is done an index could be established indicating the final barrel to action line up and chambering is next.
The question of Acme or square threads is purely academic for this project because you couldn't rethread the action.