Is there an easy way to mirror a pre-existing shapekey animation/action?

I created a series of shapekeys to animate some clothing on one side of the body to make sure everything was right, set up the actions, NLA, etc. Then I created new shapekeys from the mix and mirrored them so that the effect would be on both sides. However, now my animations only run on one side of the body. Do I have to redo the animations from scratch with the new shapekeys, or is there a way to copy the keyframes on the timeline of the old one sided shapekey to my new mirrored shapekey? The only data I need to transfer are the frame and the value.