I think if I was going to give this a try I would look for a backpack with a mesh outer pocket. Something like this:
http://www.thenorthface.com/webapp/wcs/ ... tionId=T58This way the inverter could go in the mesh to allow some airflow. I'd put the battery inside the main pocket or hydration bladder pocket low and tight to my body. I might try running the battery leads together in a piece of split flex tube to the inverter. You could probably even cut a small hole and go right through the pack so that you don't have the leads on the outside where they can get caught on something. Also figure out a way to cover the electrical contacts on the battery and inverter for a little extra protection, maybe just some good electrical tape.
I also might be inclined to go with a smaller battery to lighten the load, even if it meant a battery change during the event. As TS mentioned, a hip belt would be a big plus too. Just my two cents... I've never actually tried this so all of my suggestions may fail miserably.