Looks like that should work. Here's how I would do it:
Get a hub with casette, and a QR first, and if you have to bend the frame to get it in do that first.
I wouldn't even bother welding the hanger. It looks like if you just move it so that the axle slots all the way into the dropout it would work too. Why can't you just keep it on the outside of the dropout and bolt it into place, but in a different location?
Grind off only the bit of the hanger that slot into the dropout. Install the wheel and the hanger, and clamp it into place with the QR, for now. Install your gears and all other stuff and check if you got the position of the hanger right. If the derailleur is too close or far from the cogs, you will have trouble. In picture 3 it looks too far off IMO, but the best way is to try with all the piece on.
In fact thinking about it, I would get a specific bolt on hanger. They make these for aluminum framed bikes. Salsa used to make nice ones, but i'm out of the bike thing for a few years now so I don't know if they still do.