Here's my take on it.
In a relatively normal checkout - not the "one hour with the instructor for rating renewal", but one for insurance/club purposes - both the checker and the checkee are normally fully licensed and legal to act as PIC. Who is actually the PIC in such a scenario is a matter of discussion between the two of them. However, when an accident occurs the authorities and the insurance companies will most likely look at the most senior person on board. So it makes sense for that person (usually the instructor) to sign out the aircraft, and sign the logbook, as PIC.
This is not your normal checkout. The instructor is not allowed to act as PIC because of the ban by the authorities - which is a can of worms in its own right. And the checkee is not allowed to act as PIC because he's not yet insured, and flight without insurance is illegal. So based on the information given I'd say that there is no way that your flight could be made legally in the first place.
There's two ways you can solve this. The first, probably most long-winding of the two, would be to question the legality of the ban in the first place. I don't know of any provision in the laws of the jurisdiction where I fly (EASA) that allows the aviation authorities to "ban" a person from flying, when he or she is otherwise fully licensed, and without due process of the law. Maybe they could temporarily suspend the privileges pending the court case, but an outright, unchallengeable, indefinite ban without a court case? I don't think that's legally possible.
The other way would be to contact the insurance company, explain the dilemma and work together to find a way to make the flight legal and insured.
One possible way of making the flight legal and insured would be if YOU were to sit in the RHS, acting as PIC, with the checkee on the LHS handing the controls, and the instructor in the back to eventually sign off the checkee. (I know that the Dutch authorities have once given permission for this kind of solution when somebody needed to do a type-rating exam for a highly complex but unique aircraft, and there were no examiners anywhere to be found with that type rating. So a type-rated instructor was in the RHS, the checkee in the LHS and the non-typerated examiner was in the back.)