What's the stage 3 head consist of?
While I agree that a HIF44 would be better (almost academically so), the HS6 will give it that period look you are after, though, if it were me, and for a period look, I'd probably run with twin HS2's given your spec and usage.
The stage 3 head consists of stainless steel 35mm in & 29mm ex valves, bronze valve guides, all ports are fully ported all the way through but not 'over ported'
If you are going to use it to 6k which it will comfortably do I would go 3.76 not 3.1, I live in a similar area to you and will never fit a 3.1
3.44 is a good all-round ratio
People are obsessed with the higher ratio diffs which the mini was never designed for...
1275 Cooper S options started at 3.44 went to 4.1
I've got a 998 in it currently with a 3.76 diff and i just find that it hasn't got the legs on the faster roads around here, it just runs out of puff and it's doing 5k revs before you know it and not really getting anywhwere but i suppose that's down to the lack of power.
I used to have a Metro a few years ago with a 3.4 diff on 12" wheels and liked the gearing on that. Using Guessworks gear calculator, a 3.2 diff on 10" wheels is the same as the Metro's gearing, that's why i suggested the taller 3.2 diff.
I am however looking for more experienced Mini owners advice on this subject, so i'll highly likely go with the 3.44 diff i already have now.
Another under-rated suggestion which would keep it exactly in period... a single HS4 1 1/2" vizarded
More flow and gas speed than a pair of standard 1950's tech HS2's
Cheaper insurance, easier and cheaper to set up and looks dead standard.
What about a vizarded single HS6 carb? I've already got a HS6 in good condition.