Conformally coupled Higgs inflation

This is another possibility which should interest minimalists: In a theory that contains gravity and the Higgs, a "non-minimal coupling" between the two fields, usually designated by the coefficient "xi", is possible. By default, xi is normally set equal to zero. In theories of Higgs inflation, xi is normally set to a large value of several thousand. But for a special, small but nonzero, value of xi, the Higgs-curvature coupling becomes conformal. Is it possible, perhaps with the right UV physics, to get successful Higgs inflation from conformal coupling to gravity? The main interest of this question lies in the possibility that the underlying fundamental theory has a conformal symmetry broken by quantum corrections, perhaps as contemplated by Meissner and Nicolai, and Bars, Steinhardt, and Turok. In this discussion thread, I have collected some technical resources on Higgs inflation which may help to clarify the issue.