Just about any mini fitted with just abut anything taller than a 3.6 will not see it`s Theoretical/potential top speed,
the good Doc is dead right, even a stock-ish cooper S will have a higher top speed if fitted with a zippy-er diff ratio (pretty well most cases)
3.4:1 final drive has a "theoretical" top speed of about 145mph & they obviously don`t reach that speed in reality do they??? --->No,,, barely able to punch past 103mph (pretty well most cases)
& Reasons are simply wind resistance & just not enough grunt.
Add """PLENTY""" more grunt & you may get somewhere close to the mark.
Make the car more streamlined & you`ll get an even better result
but just adding a taller diff ratio with only make you go backwards,,, well ok, maybe not actually backwards, but you should get my drift, yeah?
Now,,, lets talk a turbo injected mini monaco fast back sprint with over 200hp & more than 5 inches shorter & windscreen raked back a good chunk & de-seam it, etc etc etc & add some skinny wheels/tyres & & & & etc etc etc etc, then i`d say maybe 150mph-ish, but would be one hairy ride
The Mini Marcos GT was claimed to have reached 141mph on the Mulsane straight at Le-Mans way back in the 60s, but it`s a bullet shape isn`t it? & it would also have had some pretty fancy go-fast gear under that fibreglass bonnet too.