I've only ridden down Rosedale Chimney twice. Both on fixed wheel. The first time I only had a front brake. Never caused me any problems but I wouldn't say that it was "relaxing"
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I found descending Hardknott in the rain (again on fixed) more tricky because the road is pretty rough. I did especially buy some grippier tyres and upgraded my brakes before I descended Hardknott. I just sat as far back as I could and took it very slowly.
My mountain bike with Hope hydraulic disk brakes would descend those hills very easily. I remember a very long 25% descent from a Welsh mountain when I was on a camping trip. It occurred to me that this very relaxing descent on my mountain bike would be pretty hairy on my road bike!
I stand up to climb silly steep hills to keep my front wheel on the ground. I did once fall off when my wheel span on wet pine leaves climbing the Devils Staircase. I fell forwards, so it wasn't far to fall and was more like leaning against a wall than actually falling over.