Allan, many forget the " 1071 " Cooper S, used when there was a 0 - 1100cc class - the " 970 " for 0-1000, and big motors for the 1001- 1300 class..
997 and 998 were of course Cooper, not Cooper S.
My good friend, the late Nell Holdstock / Donaldson had a 997 long stroke Cooper, from memory also a 1962 model, here in NZ,as well as her 1961/62 Austin Healey 3000 Tri-carb which she brought from Canada in the 1980's - Healey is still here, Unsure what happened to the Cooper.
Here is Nell, with BMC BOY, looking at the Cooper Formula Junior single seater that Nell owned but sold to Ross BMC BOY many years ago, It is being rebuilt/restored. The Historic Formula Junior recently did a Garage Crawl looking at projects under way.