Honest question (I am totally ignorant about these things): If you did this, would you be able to accept patches from the community on the open core? Or would releasing your proprietary code violate the GPL of the coder who sent the patch?
If the core is a library, and licensed under LGPL, the proprietary add ons can dynamically link to it without issue. You could take community contributions. This would not be true if the library was GPL. Anything that links to GPL has to be GPL compatible (make source code available).
If the proprietary addons are libraries and the core links to the addons, the users could violate the GPL when they link to them, unless you as the original author of the core, specifically enumerate the addons in the license you distribute to them. You would not be able to take community contributions in this case.
If the core communicates to the addons without adding the addons to its assessable region, such as talking over pipes or sockets, you would have no licensing issues even if the core is GPL and has taken community contributions.
In this case, you can choose the license for your own binary distribution. And you can change the license if/when it becomes necessary.
You then transfer the license to an oversea entity that then licenses back to your majority owned company.
This is the professional business with software licenses as there is no physical good to ship, it is in principle a good way to transfer money accepted as a common business transaction (paying licensing fees), supported by tax laws for international trade (e.g. often various tax exemptions).