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Different people here have posted different opinions as to whether or not you'd notice the difference between 32 and 34, but if somebody offers to give you either an 11-32 or an 11-34, take the 11-34, just in case.
So you've gained 1365' in 2.92 miles. You plug that into your handy/dandy incline calculator:
and you get a incline of 8.8%,(which seems awfully low for that hill)
Now, the math is the math. I'm sure the incline calculator is giving you the right % for the numbers you put in.
Are any of the touring models you are familiar with sportier than others and would give a better unloaded road experience?
If you are worried about flange breaking use a large flange hub.