OK everyone, back to work. Quantum Gravity is not going to figure itself out!
In which signature is the “conservation of convention law” stated?
‘I know, I’ll use Latex macros’ Now you have two problems (also see https://xkcd.com/208/ and https://xkcd.com/927/)
hopefully you are using the maths convention — phi_^* for pullback since it is a “dual map”
there are worse convention-violations in GR; signature, Riemann tensor, extrinsic curvature… comparatively this is not a big deal!
because it is consistent with the index positions for objects being pulled-back, forms, vs objects being pushed-forward, vectors.