Question: Tetrads and Levi-Civitas

In the realm of tetrads where both world indices and Lorentz indices are present, contractions, say, using simultaneously the Minkowskian (galilean) Levi-Civita symbol,

and the curvilinear Levi-Civita (pseudo-)tensor,

can be considered. Although each of the two types of Levi-Civitas can easily be obtained separately by specifying Setup(levicivita = galilean) or Setup(levicivita = nongalilean), I cannot figure out how to have them both available at the same time. Any suggestions?

PS: I am, of course, aware of the fact that the two Levi-Civitas are related by some appropiate square-root of the determinant of the metric, but I have no desire to fiddle around with explicit such determinants if they can be avoided.