you can't. If it is anything like my Grandad's problem it was just wear and tear. Nothing about how it has been driven. Things break eventually. My uncles old Golf perfectly maintained looked like new broke eventually.
Top ratio is the same (or near enough), and 1st is about the same too. So in other words you just have to change gear more often for no real gain. Arguably the car will be a bit quicker in each gear, but the more changes more than cancels that out 98% of the time.
The 6 speed gearbox (as with any gearbox with more than 5 gears, and most with more than 4) is just a ploy to sell more expensive versions. By calling them the Sport.