My question is, can you really spin your crank that fast and stay upright on a prolonged climb?
Yes. My gearing goes lower than any combo mentioned so far (22/36). I have zero problem staying upright or moving forward on big hills. Remember, you are fighting gravity while climbing a hill, so one's cadence slows. On a 15% grade carrying 20 kg, you won't be spinning too fast!
I find the challenge is getting started again after stopping. But once I am moving, no problems.