Ok, after finally figuring out what to search for I found an answer here:
http://answers.unity3d.com/questions/623878/how-to-restart-mecanim-state-animation-or-play-it.html
What I needed to do was create a script with a reference to the animator that called:
myAnimator.Play("Roll", -1, 0f);
This lets me press the button as many times as I want to restart the animation. I hope this helps someone else!
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