I have zero experience with any M16 engined Morgan, though note you typed that the starter did not disengage after the engine fired up..?
That being the case there is just a chance if it uses a relay in the circuit to supply the solenoid mounted on the starter with power, then as happened in my +8 the relay contacts can burn a bit over time and thus intermittently stick closed/on, causing the starter run on you describe. If that might be what happened to your Morgan, then replacement of the relay (if fitted) might be worthwhile insurance..?
Just thinking in type.
