It's perfectly legitimate to do the instructor flight in a group owned aircraft (either remunerated or un-remunerated), as it's not instruction for the issue of a licence or rating.
I do several of them every year. The insurance will nearly always cover an instructor for re-current or continuation training.
You can also dedicate the hour to any exercise(s) you wish, it doesn't have to be a mini-LPT, so long as the aircraft is suitable for the purpose and the instructor is happy to fly it. There was an old requirement for instructors to have 5 hours on type before instructing, but that no longer applies.