As already said, the HSC rules are based on MSNZ T&C and Schedule K. Nothing else. There are already many cars in NZ built to these rules. The MSNZ rules stipulate:
Only tyres suitable for legal road use in New Zealand, or period and
tread pattern correct, bias cross-ply tyres (refer note) may be used.
(ie. road tyres having 1.5mm minimum tread depth across 75% of
the width of the tyre and around the entire circumference). Aspect
ratio is restricted to 50% minimum. The use of semi-slick tyres with
only radial grooves is specifically prohibited.
Note: An example is Dunlop CR65 brand tyres
Really, there is nothing to be gained for the class as a whole to allow either one car, or the entire field, on slick tyres. Although slick tyre technology did begin to arrive within the period HSC has been structured under (pre December 31 1977), the vast majority of these types of cars raced on treaded tyres. When there is ample availability of both DOT radials and treaded bias-ply tyres, why have slicks? It really comes down to wanting a performance gain. If the whole field is on slicks, it negates any performance gain. But, why bother? Slick tyres create extra grip, which then puts greater stress through the drivelines. This is turn creates more unreliability. And for what? Also, slicks have a shorter performance lifespan than treaded tyres, so replacements are required more often, thus increasing costs.
Remember, this is only historic car racing.
Gerald, the photo here shows that sometimes your AMCO Mini did race on treaded tyres. Also, when you say you want to race it on slicks because this is what it raced on in period, I'm guessing you want to race on radial slicks, and not bias-ply slicks? I can virtually guarantee your car didn't race on radial slicks in period. It would have been bias-ply slicks. The technology between the two are quite different, and indeed, a Hoosier treaded bias-ply would be closer in technology to what your car raced on in period than a modern radial slick.
Remember, HSC is never going to be all things for all people. It'll either appeal or it won't. The great thing about New Zealand is that there are so many different classes to choose from. This class only creates a haven for those wanting to build and race T&C and Schedule K cars under MSNZ historic rules. I know I don't speak for everyone here, and people go historic car racing for different reasons. But for many, the appeal in racing a 45 year old car is that it looks, feels, and handles like a 45 year old car.