Okay, that's why this is in the Inbox. I started to formulate my question in long words in email, but decided this was the quickest and easiest way to ask it. :)
Okay, so this is definitely not the place to fix my problem. So I will instead try putting something into SketchMorph's veryDeepFixup: which will ensure its underlying form gets copied when I green-halo a SketchMorph. SketchMorph is an exception because he's a dumb data object, not a "player" who wants to share a costume.
-- I was working on an icon, writing scripts to change colors pixel-by-pixel, goofed up my "backup" SketchMorph I had torn off the green halo, only to find I corrupted my original, as well. Some work lost.