Camera and Binocular harness
I've been looking for the same thing and the best I have come up with is the dual harness that is designed to hold one camera on each side of your body. It would require an adapter for the binoculars but that should be a fairly simple fix IMO. I have not committed to any thing yet but that is the best idea I have so far for birding with a camera along. Please let me know what solution you come up with.
Reality is that which, when you stop believing in it, doesn't go away.