You have nailed it except for one critical factor
The magnet size .
There are 2 sizes ( $ if you include Vanguards )
So when you see an alternator listed as 5-10 Amps that is 5 with the small magnets & 10 with the big magnets.
All stators are interchangable
The other thing to veriify is the carb solenoid is energised.
I ran a power wire direct to the solenoid one time & found the solenoid was not opening
If you go direct to the solenoid please put a fuse in the wire so if it shorts out the alternator does not continue to energise the wiring till they melt.