You could have gotten the rear wheel to center perfectly by brazing the two ends of the replacement section separately. Do the 2 middle sections together first making sure in your mock up before brazing that it is a bit long. Now use a true wheel to see if the seat stay length is right (so the wheel centers). Hopefully it is a still a little too long and you slowly nibble a bit of the dropout away (so the distance shortens) until the wheel does center. Do this slowly checking often so you don't go too far. It is possible to pull the dropout out of the seat stay to file it some more. If the chainstay gets sprung too much so it loses contact with the seat stay, it can be bent back up when out of the seat stay. Of course you need to check that the dropouts are the same distance apart from the centerline of the frame with the Park ***-2 Frame Alignment Gauge (or something similar).


By the way there isn't a need to slot the seat stay into the dropout for this repair. It is easier to braze with an open end and extra brass can be added beyond the stay to create the dome (or whatever shape you want). It isn't going to come apart.


In this case I would absolutely have spliced in a piece of seat stay to preserve as much of the original frame as possible. I've done a lot of rust repairs over the years and often a tube is not rusted evenly throughout the tube but just in certain areas and usually near the bottom where water would sit. Once you get the stay cut apart, you can look into the rest to see if it is rusted too much to save.