I'm very interested in this project as i want to do something very similar to dynamically balance 1/4 inch end mills after i resharpen them. As you and others have said, synchronizing the ADC conversion to the index pulse is going to be quite difficult.
I'd recommend using two identical ADC chips driven off the same digital IO to enable conversion. I'd use the index input to trigger that signal line. And I'd make a bunch of samples at one RPM and a bunch more at a second RPM. Keeping in mind that the sample and hold circuity of the ADC's might have a millisecond or 10 delay from the index pulse and so you'll need to filter those 'flyers' out of the digital data. And then it's w matter of modifying the rotating mass and seeing if you've guessed correctly about how much delay you've got between index pulse and 'sample and hold' capture. The two different rotational speeds should help with that, unless of course you're dealing with some fun harmonics and Nyquist frequency issues.
Dan.