Hmm, I figured this leaderboard would mostly appeal to the "any%" runners with the addition of the in game leaderboard so I kept it pretty bare bones to start off. I'm not opposed to it, but I would prefer to see some interest first rather than just adding more empty leaderboards.
run splits as administrator? No other ideas sorry, there are more general streaming/speedrunning forums on here that you might find your answer in.
AFAIK it's not possible to show splits over a fullscreen game unless you have them on a second monitor, so you might have to switch to windowed. As far as global hotkeys not working, I have no idea because they work for me even fullscreen. If you aren't using LiveSplit you should try that.
In story mode the in game timer only keeps track of individual levels, so I'm not sure what you mean about it being synced. And if you can be more specific with the problem you have with splits I can try and help I guess but just your standard timer is all you really need so I can't really guess where you've gone wrong.