Do you have part ownership of the plane? Or just fly a group aeroplane for a set hourly rate?
Have you read the insurance document? Any mention of limitations for anyone to teach on it? Any mention of a checkout required for an instructor prior to teaching in this particular aeroplane? Under what category is the plane insured?
These MAY have something to do with it... I would seriously consider not going through with getting your own instructor in to sign off your VP differences in that plane, just from the standpoint that I believe they want / need you to have some teaching uniform to others flying the plane. For instance, cruise settings they want you to use to enhance the life of the engine, specific instructions about particular checks that may not be standard for the plane type, any non standard instruments / lights / engine management system / other items that you may only know whilst flying with someone who already flies in that plane, how you should leave the plane after you have flown.... etc....
It may sound petty, and I do agree with you that surely a well experienced instructor may very well be more than capable at teaching you about the type. It is important to remember that every plane is different! I remember an instructor teaching me on a new type some years ago, and he didn't seem too familiar with the plane despite him having flown that particular plane more than 40 hours (albeit some time ago) there was a digital engine management system that had been installed and he had no idea how to use it - which is somewhat worrying...
I think you should probably just bite the bullet and wait for the group instructor. Groups have a tendency to have a lot of politics... I'd go with the flow for now and then when you've flown the plane, get your instructor in! :-)