After some additional experimentation, I found that another way to expand the edges with “less jagginess” is to use these steps instead of the Magic Wand:
- Select all: Ctrl-A
- Float: Ctrl-F
- Defload: Ctrl-Shift-F
This seems to retain at least some of the “fainter pixels”, unlike the Magic Wand and when you expand the selection, the edges might be better than with the Magic Wand only.