Originally Posted by
pgoat
....My guess is even if a welder can join the two halves, aligning the rear end for shifting and a straight chainline would be difficult or impossible
The right way to do the job is to straighten the damaged area and align everything, and fixture it that way before welding. Then a minor tweak may be done afterward if it's necessary, but nothing worse would be needed.
If the remaining section of your hanger is hopeless, a hanger can be cut from any similar dropout (need not be identical). Keep in mind that a welded hanger will not be as strong as a complete dropout replacement would be, but no great strength is needed, as witness all the aluminum hangers out there these days.
I don't know if he welds hangers or only does replacements, but you can send a photo of the broken dropout to Andy at Yellow Jersey in Wisconsin. He does excellent work at reasonable prices which might make a repair feasible.