I feel your pain. I was recently hacked yesterday (though luckily, did not get a name change), and was charged $75 in MS points. When I called customer service, a nice guy helped me out and explained that they could do the investigation (which takes 3-4 weeks) but that it also meant I'd be locked out of my account during that time frame.
I decided to just eat the charge (I need the Netflix with no cable at the hosue), but have my credit card removed. I then noticed I had to recover my gamertag as well, which I did, then watched an episode of a TV show on Netflix. After the episode was over, I encountered the same error, so I recovered my tag once again, then changed the password.
Then today, everything has been working great, but I noticed my MS point total being much lower than it was. Checked my download history and discovered 5 different XBLA titles downloaded, obviously none to my console. Called back just a bit ago, decided to go through the investigation.
I'm a bit disheartened over the security breach, and probably will never purchase anything digitally over XBL again with a credit card, but I do have to say the customer service people are very well tempered, nice, and have understanding attitudes.