You're rabbeting. Lots of good advice here, one of the best pieces is to take out the bulk of the material with a circular saw first, trying to take that much meat with a hand router is a recipe for blood.
As for rabbeting bits, you're probably not going to be able to find one that would do a full inch cut, so instead you need an edge guide (another board clamped to the post that the router base can run along) and something like this:
BUT, that all said, you would probably have just as good a time hogging it mostly with a circular saw then hitting it with a hand plane to flatten out the leftovers.
If it was me doing this project I would draw a line on the wood freehand roughly following the curves of the wood. Then I would use straight router bit similar to the really cheap ones I'll link below. I'd follow that line cutting with about a 1/2" wide bit. I'd probably do it in two passes so first pass cutting 1/2" depth then second pass cutting a full 1" depth. Last I would use 100 grit sandpaper to smooth over the machined corner of the groove into something more organic looking to match the piece.