We're building exactly what you're describing at http://www.swish.io (available on both ios and android) We organize clips by plays, teams, and games and annotate videos using the meta data from the play-by-play. We even have the slo-mo slider capabilities you mention, if you check out our app you can press down on any video and move your finger back and forth to watch in slo-mo (works much better on iOS at the moment).

We source our content from social media, not from the league's sites so we do not have every play but we have a lot. Usually 30 or more per game.

If you're a sports fans try it out would love to hear your feedback!