What are you talking about? I've only taken one course in quantum field theory, but I've never heard of anything where quantum mechanics was not linear. Can you give me a citation? It seems to me that failure of linearity would either be irrelevant (superlinear case, low amplitudes) or so dominant that any linearity would be utterly irrelevant and the Born Probabilities wouldn't even be a good approximation.

Also, by 'the Schrodinger equation' I didn't mean the special form which is the fixed-particle Hamiltonian with pp/2m kinetic energy - I meant the general form -

i hbar (d/dt) Psi = Hamiltonian Psi

Note that the Dirac Equation is a special case of this general form of the Schrodinger Equation. MWI, 'naive' or not, has no trouble with variations in particle number.