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My 2 speed, on your road, made me deploy the 24inch gear - luckily, I don't go up there very often. Around town, the rest of the time, the 2 speed is absolutely fine.
Another plug here for Chris Compton in Catford.
ETA If you want to try my 2 speed, S-barred, Ti, you're more than welcome to, but I think you are taller than my 169cms, and my seat post is maxxed out.
I'm down the hill and over the railway line from you.
Asked predominantly to those who own such a bike, and have visited my house.