I don't know what we as a group do between seasons, but we could have some sort of fun series where each race is with a different car-set, and it could be a simple practice/qualification/race format to make it easier to administer. We would get a rough idea who liked what the most, and use that to decide what to do next.
I have yet to try the MP4/13 so can't comment, but I do quite like the Formula Renault as I find a modern F1 car to be more of a test of reflexes than anything else, so I'd rather avoid that if possible.
We could also use circuits that are not on the F1 calendar too, like the old Silverstone, Brands Hatch, Rouen, etc. with driver safety not being of any consideration to us. Please don't hate me for saying it, but I even quite like the odd oval race, which each of the two previous leagues I was in (even the European one) included in their championships.