Came across this post in 2017, and for future readers, wanted to suggest a useful resource: Autodesk's Bonus Tools.
They're in a free, downloadable package from Autodesk, and one of the included scripts provides a GUI for reversing animation keyframes without using a Dope Sheet, re-animating, or coping individual keys.
Maybe I was under a rock for a while, but just started using these and have been satisfied with the results.
Link is:
https://apps.autodesk.com/en/Detail/...50172702393827
Cheers.