I signed up for this forum solely to say THANK YOU. I spent over an hour trying to sort this out until I saw your post. As soon as I skimmed through it, I realized I was in exactly the same boat: with both a personal and an organizational Google Account with the same e-mail address, thanks to all this Google Apps foolishness. I followed your instructions, and the minute I changed the password on my personal account, my phone buzzed with the account login error message. A few quick taps later, and I was in business.
Somewhere, I hope some Google engineers are kicking themselves for not getting the Google Apps integration done properly the first time around. What a nightmare.