This may not be the "correct" answer, but it's what I find works:
Since Sk.globals seems to gets re-initialized when the program is run, the best place I've found to store this kind of information is in Sk.builtins.
For example, to make the below work, try this:
Sk.builtins.INJECTED_CONSTANT = 'Hello, World!';
or even better yet:
Sk.builtins.INJECTED_CONSTANT = Sk.builtin.str('Hello, World!');