Another way might be for an editor to have two sets of line numbers - the normal set plus a set which is "the line this text was on the last time it was loaded or renumbered". Then you can fix the errors in whatever order you like, and only the editors need to change. Navigating could get confusing if fixing early errors entailed moving lots of code around, but that's a problem with negative numbering too.

The old DOS assembler A86 had a rather different way of solving this problem - it injected its error messages right into the source files! It actually worked surprisingly well, but it would probably cause too much confusion these days.

Agreed about editors having a mode where line numbers don't change until you hit the magic button. That would be potentially very useful, while probably not too much trouble to implement.