If you already know that your 70-200 isn't fast enough, I don't see what the discussion is about. I've run into the same limit with my f/4L, and the best you can hope to do is shoot manually and in RAW, try to pick an area with better lighting than the rest of the rink, and then hope you got enough light to salvage in post. Of course, the ultimate hope is that you'll be shooting in a rink and not the equivalent of a dark cave.
That's not always an option, so the 50mm f/1.8 comes out of the bag. And, as I'm sure you've been able to discover on your own, the 50mm f/1.8 doesn't have nearly the focusing speed of the L glass. Fast shutter and a wider aperture doesn't do you a lot of good when you're OOF. You'd almost be better off trying to pan with the L glass.
It sucks, but you really don't have the right gear between the f/4L and the 50. I know I still don't have the right gear.. but I'm getting closer. Another 50 (not the slow focusing f/1.8) would work out well, and the 85mm f/1.8 is another prime option, but your best bet would either be a 70-200mm f/2.8 lens or a 50-135/150 range lens.
I find my best hockey photos come from either my f/4L in well lit arenas (sometimes you just have to admit lighting defeat and only shoot in the lit portions of the arena), with my 18-50mm f/2.8 (although that really limits you to where you can shoot and what you'll be able to cover), or a borrowed 85mm f/1.8.
If I were you (and going by the fact that you don't think you need the reach of the 70-200mm), I'd invest in a Sigma 50-150mm f/2.8 lens.