Your experience so far is succinct as boith methods are good, but not perfect. In Devon, in a mild winter, it should be fine outside.
But if lots of frost is coming, say -5C and lower, I would hatvest roots and simply put them in paper sacks with a little soil still on, to conserve moisture. They could be in a garage where slight frost may happen, which they can tolerate, better than indoors where warmth makes them sprout and go soft.
Clamps are for large estates and commercial producers, not appropriate for gardeners.