Have you tried to Break Apart the text twice to turn it into splines?
I'm changing the text with action script, so I don't think I can break them apart.
If anyone else is having this problem. I wasn't able to get the animation to stop distorting the text, but I did come up with an ok solution. I created two textfields. One text field gets rotated and the second text field gets displayed when the rotation stops. This way when the card is still the text looks crisp.