Sorry, I stand corrected. You guys are correct. Ten years at most.
Nitpicking here, but I think you're wrong about this:
...no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President more than once.
So the way I read it, two years precisely, you're still eligible to be elected twice. Two years and a day, you're only eligible to be elected once.
So the possible legal limits on length of service (barring getting back in via succession after all eligible elections) range from 6 years and 1 day (or possibly, any portion of a day), to 8 years, to 10 years.