You mention oil change every month but you don't mention miles. Only in your hypothetical, theoretical scenario do you mention miles.
You need to be more specific as to how much oil is being lost. Then you need to be sure there are no leaks, or are you burning it. Compression test will tell you a lot but isn't an end all. Could be simple as valve seals. And yeah, if you're burning a quart a week (500 mile assumption), then no, you don't ned to change oil every 2000, just the filter, if that. But if your burning that much oil 1qt/500 miles, you aren't going to be using that engine long.
That said, there's no benefit to a rebuild over a JY engine. You need to change standard oil 2000-3000 miles, anything higher is no go. Synthetics especially pure, can go longer intervals before it breaks down. Mobile 1 (Synthetic Blend) is changed every 5000-6000. New filter every time. Only way I'd do a rebuild, machine shop special 3800 is if I were attempting to go where no 3800 went before, lol.
