That correction is exactly the way I would reccomend it. Your original diagram has too many places an unwanted voltage feedback might happen. The 1-wire alternator has its detractors, but other than needing a one-time goose on the throttle after startup, it's the simplest way to make the swap. Good luck on the rewire!
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
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