I'm confused by this question: Why can't General Relativity be written in terms of physical variables?
I can't quite see how you can make any change to the metric without either: (a) changing the physics; or (b) changing which point in your manifold represents which physical point in spacetime. Either of these would, it seems to me, disqualify the change as being a gauge transformation, at least in the usual sense.
So is there some cunning way of changing the metric that avoids either (a) or (b), or is there some sense in which (b) can still be thought of as a gauge transformation?
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