I don't think it's the tension in your chain that's causing you problems. The chain on my singlespeed is so slack that you can freewheel the cranks backwards, but it never drops off. I don't think there's much point in getting a half link either because as soon as your chain wears a bit it'll go slack again.
If you're sure that your chainline is OK, then maybe your brivetrain's a bit worn. Using un-ramped chainrings also helps, although I've quite happily used Deore ones in the past too.