Hm... Maybe I was a little too quick to write my own question... Reading a little more in this forum, I was inspired to try something.

For others encountering this problem:
Save the shared code in a .dotm file, not a .docm file

Advantages: The problems above disappear
Disadvantage: Development becomes a pain in the ... arm, as you can't see the code in the reference when testing a form instance. My workaround will be to use .docm during development, then change to .dotm when rolling out to users.