There were a couple of things I had to do, but I now have the player running/launching as it should:
1) Delete the player AND PLUGINS for the classic version (so, yes, it seems you have to choose, you can't have both)
2) In the Protocol Helpers of the Preferences panel (in IE), add "mms" then choose the OS X version of the player as the default application.
I know some people have had issues where removing the Classic player didn't work, but it worked for me!