I don't have a credibility problem here or where I work, but you seem to. I have worked in this industry for 50+ years and while teaching worked directly which major equipment and engine companies. You were an auto tech and you saw a problem, but just let it go on and get worse instead of looking for the cause. You don't want to pay a pickup and delivery charge when the problem first occurs, but will put it your pick when it gets bad. I have worked with Toro many times on units that were out of warranty and in my experience a good service tech, documented problem, and Toro support will work together to solve problems at little or no cost to the customer. Honey works better than vinegar works better when trying to resolve these problems, and with reasonable people the odds go up. I'm willing to bet your original problem was the result of cylinder head problem, which I our shop would have cost about $125. I'll also bet Toro would have covered all or most of this, for a good customer and dealer.
Finally because a teacher needs to work with every student, no matter how they act; Briggs engines do not have a 9V alternator on their engines for charging. They use a few different types of 12V stator and voltage regulator systems, depending on the size and model of engine. Maybe I don't need to tell of this as you already know that a 9V system will never keep a 12V battery charge properly. Also, need to warn you that depend on which engine you ordered, major alterations may be in order due to muffler size and configuration.
Finally because a teacher needs to work with every student, no matter how they act; Briggs engines do not have a 9V alternator on their engines for charging. They use a few different types of 12V stator and voltage regulator systems, depending on the size and model of engine. Maybe I don't need to tell of this as you already know that a 9V system will never keep a 12V battery charge properly. Also, need to warn you that depend on which engine you ordered, major alterations may be in order due to muffler size and configuration.