I didn't know that quantum decoherence tackles the measurement problem. It seems like quite an intuitive explanation and does preserve a global wavefunction.

Perhaps this doesn't quite count this as "standard quantum mechanics though. As I understand there is a very tight-knit theory consisting of a mathematical model (Measurements are self adjoint operators on a Hilbert spaces, unitary evolution given bx the hamiltonian, states are unit vectors or POVMs.) together with a physical interpretation that amazingly fits the observations.

This + quantum decoherence seems more in the realm of mathematical theory with a nice interpretation and some experimental evidence.

And the thing you're measuring is already entangled with the messy universe around it...