You don't need to have a global entity id at all.
The #registerModEntity is the right one.
This is totally correct.
Also, while it doesn't give you a vanilla egg, it doesn't stop you from making one.
The lazy step would be to register a global entity id and add it to the vanilla egg list. (but then the local id registration is far less interesting)
Another solution is to create your own egg, like any item (see ItemMonsterPlacer, though you'll need to replace the global entity id lookup with either entity name or local id).
Another solution is to use events and spawn the entity yourself.