JRiver is, in my opinion, a bit like Apple. They do what they do VERY well. Everytime I turn around, they have revamped something. Yes, it's something I really like, but not necessarily what I've been begging for. What they do is generally magically chosen.
Remember, they have to be very careful with their features because the program is already so feature rich that it could easily become unmanageable. Space bar for playing only makes sense to me in a player like VLC that doesn't manage a library. In a media management library, you want more elaborate keyboard shortcuts because space bar would be used for typing a space in a song title, for instance, and the average user might wonder why it doesn't work when editing a title...or not realize they are editing a title at the moment. It's complicated as you might imagine.
Try a macro program. I use Macro Express (commercial product) and it lets you activate a macro with a basic key, like "2", and I bet space bar would work. Then, create a simple macro that just pushes Ctrl + P when the macro is run (run by hitting space bar).