I have not been able to start the game from Steam without disabling the Steam Overlay UI (seems like it's unique to my computer - running windows 7 64x).
I've tried a steam support ticket already, with the response pointing to a failed solution that I've tried all too many times (disabling Anti-viruses etc.)...
Is there a way to start SK by itself from it's installation folder? As of now it's the only way for steam overlay to work without having both the game I want to start as well as the overlay to both not start (not crash)? (it worked for portal 2 and it's own execution file)
You can try the instructions here to get up to date Java files that my not have a conflict with the Overlay.
I don't have any confirmation on this succeeding yet. So far it's just another troubleshooting step.