I cannot speak to elevation concerns, but my 5-speed Cooper does pretty will in the mountains of Vermont (which top out around 4000'). If you're talking about the Rockies, and elevations around 10,000' that might be a concern.
Yes, an S would be faster. Yes, you have to shift a Cooper a lot. Yes, it's a lot of fun.
If you're willing to grab second gear at 40mph, everything's fine for spirited driving. If you're trying to hold 4th gear at 40mph, you'll have problems.
