I think a helmet-mounted camera would give the most interesting perspective and would be fairly easy to put together.
One option that popped into my head is to figure out where on the helmet you want the camera mounted, drill a small hole and run a 1/4-20 hex bolt through the hole with the threaded end poking up outside the top of the helmet. Use a stop nut (again on the outside of the helmet) to hold the bolt in place. You would need to select a long enough bolt to have enough thread left to screw the camera tripod mount into. Maybe another loose nut that you can back against the camera to hold it tight at the orientation you want (i.e., head-on, slightly to one side, etc.).
Hopefully the helmet would have enough padding that the head of the bolt (inside the helmet) wouldn't make contact with your noggin. I'd still add some kind of leash that attaches the camera to the helmet strap just as a back-up in case it works itself loose somehow.
The potential drawbacks to this design would be it likely voids any warranty on your helmet and may or may not affect its structural integrity. Also would have to set it up before you get started on a paddle or whatever (i.e., screw it on, turn it on, get to the right settings, press record, then put your helmet on and move along).
If you search mountain biking forums, you might find some other ideas. I did a quick search for bicycle helmet camera mount and there were at least a couple of commercial solutions available as well as homemade ideas (including some kind of carboard and duct tape chest harness!).
I'd be curious to see what you come up with.
