I went to the NAPA auto parts store and got a new battery, a 12 AH this time. It was actually cheaper than the std 5.6 AH they had. Had to drill one additional hole, and tap 1/4X20, to mount and secure the slightly larger new battery. It really spins the engine now and starts right up. Half the problem is solved now. Still only about 6 volts output from alternator. I retested the rpm's with my Treysit tachometer. I don't use it enough to be really good at reading it. Apparently there are two sweet spots on the vibrating wire. The second one I found, was at 3300 rpm, so I guess that is the correct one. Still, why only 6 volts on both alternators?
Your small 1/2 amp alternator is only designed to charge a battery in the 5AH class,putting a much larger battery on the machine ensures that it will take damned near an eternity to fully charge,and probably won't.The formula is usually 1/10 of the battery amp-hour rating for continuous charging,thus they chose a 5AH battery.
What are you using for a meter?I believe the reason why your voltage reading could be low is because your alternator is only half-wave rectifying the ac output.That's why your meter is reading an AC voltage AND a DC voltage.The choppy DC coming out of the alternator reads as an AC signal to your meter.
Try putting your meter IN SERIES with the alternator lead using the current test feature(use appropriate meter jacks).You should get a continuous reading of approximate .5Amps at full throttle.The alternator is designed to be a trickle charger only.These alternators shouldn't be relied upon to fully recharge a battery in the spring,I apologize if you're already aware of this.
I have a DR trimmer with a 6 horsepower engine that's equipped with electric start.It has a 350ma(.35amp) alternator and uses a 5AH battery.At 3500 rpms it will charge at about 350ma.as designed.The only test Tecumseh offers is ensuring the voltage rises above the battery voltage when the engine is running.I test it with a Fluke 179 DMM which is a very sophisticated meter.I've never tried testing with an analog or a cheaper DMM,as I don't own one.
I find that I,too can't always get the engine to start with the electric starter.The battery has to be damned near fully charged 12.8 volts or it won't turn fast enough.My engine doesn't have a choke,a primer only.So I found that if I open the throttle wide open when cranking,it starts much easier.
Also keep in mind,like everything else today,lead/acid batteries are not created equal-you get what you pay for.I found that the bargain-house 5AH batteries just don't have the balls the name-brand ones do.
EDIT:I somehow missed the post where you said you got it sorted,but some of this may still be useful.