I welded aluminum for several years in industry and really felt this job was do-able. I acknowledge there's a risk of messing up the soldered core but figured the heat could be shielded from spreading by using wet rags. Years ago they used to sell an asbestos fiber material that came in gallon cans. It's purpose was to prevent metal distortion while welding. I used it quite a bit doing bodywork. Obviously no one would recommend using it today.
I do know of one radiator shop that's within 20 miles that might take on the welding. Although they have a good reputation for their work, - it's not usually pretty.
