I don't see the point of creating a new class in the hopes to have a class that the "standard" 7 can be competitive in. I think that it would be better to just have the DM rules redefined, and separate from the prepared rules. With any class beyond the stock classes, there will always be possibility of someone building a purpose built autoX car, taking advantage of all of the allowances allowed by the rule set. I don't see how it would be possible to define a rule set that would allow sevens/locosts/caterhams, and not allow a purpose built car. If you truly want a competitive car and don't want to hack up your seven, leave the seven at home, and drive a competitive stock class car.
As for tires, if you create a new class and restrict it to DOT legal tires, then the tire choice is quite limited in the smaller sizes. The DOT legal tires like v710s favor large cars with large diameter tires when it comes to sizing. There are no wide v710s (>225 width) that have a diameter less than 24.6". If you allow real slicks, then there are plenty of tires choices out there for the sevens.
I don't intend or expect the locost that I am building to ever be competitive in DM on a pax basis/class winning basis, but this won't stop me from building it, autocrossing it and having a good time.
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Brian