Howard,
Let me first of all say, that this situation is outside of the requirements for the PMP exam. You should not come across a scenario that is this complex on the exam. However, you may come across similar questions regarding who is supposed to sign the charter. So let's see if we can figure this one out according to the PMBOK Guide. Regarding the charter you wrote:
...it has to be signed by a person that is external to the project and that has the authority to do so.
But there is a much more important sentence about signing, and that is: "The project initiator or sponsor should be at a level that is
appropriate to funding the project." In other words, the person who pays signs the charter.
In my personal opinion this always means the "ultimate payee". So even if there are three levels of contracting and subcontracting between you and the ultimate person with the money, the charter should be written for them.
So my recommendation: Figure out who is ultimately paying for it and that's the perspective you may want to select.