I finally swapped batteries with my Exmark and the Cub started and ran fine. I then went to Auto Zone to get a new battery. The guy there tested it first and said it was fully charged and fine. It took some convincing to get him to agree to a swap. I also upgraded to a better, crappy 'Gold' battery for an extra $29. Installed it and everything is good.
What worries me is that the original battery I bought 5 weeks ago was fine too at first. Is it possible there's something else going on that would not only drain the battery but kill it?
I checked the output of the stator and it looked correct at about 30 vac.
hlw49, If it matters at this point, I have an Astron 13.8 v / 7 amp continuous power supply that I energized it with. When energized, I got continuity.
Thanks all!