Is it possible for an AppleScript .app file to retain its custom icon, even after edits have been made to the code?
I followed your exact same procedure and found the exact same problem on operating system Sierra as well. After trying a few things I decided (in addition to changing the main Applications icon in the get info window) to do the exact same thing in the get info window of the applet.icns file and change it's icon as well.  I then opened that script editor app in scripteditor and saved the file.  The new icons remained as I changed them.  Tested in script debugger also and my custom icons remained untouched.