The idea of Liam to first apply GLV and then the “fake GLV” by doing a half GCD in the number field \mathbb{K} works for curves of j-invariant 0 and 1728. Basically the half GCD in Eisenstein and Gauss ring of integers works the same as in \mathbb{Z}. Here is a working example in sagemath for secp256k1 (j=0). However it does not seem to be working for Bandersnatch \mathbb{K}=\mathbb{Q}[\sqrt{-2}] as the geometry is different. So the remark on Jubjub/Bandersnatch still holds IMO.
This would question the choice of Bandersnatch (an embedded endomorphism-equipped curve over BLS12-381) over Jubjub (an embedded curve over BLS12-381 without endomorphism) for Ethereum Verkle trees.