First, the linear Bz field is only an approximation of the field in a SG device. You can't really have a quadratically increasing potential out to infinity.
--it would be fine if it only kept going for a finite range of x, if wide enough (as I'd said).
Second, if you did all you've shown is that the electron could be accelerated to high energy by the magnetic field acting on it's magnetic moment. But an electron won't decay all by itself just because it has lots of kinetic energy. The kinetic energy is frame dependent. A suitable Lorentz transformation to the electron's rest frame reduces that energy to zero
--sorry, by that reasoning you would conclude a large E-field would not create pairs, because E-fields can merely accelerate electrons to high kinetic energies, which means nothing. Wrong: The "Schwinger limit" is the well-accepted statement that an E-field creates pairs if E*(available length) > 1.022 MVolts. The Schwinger creation is rapid if E * e*hbar/(m*c) > 1.022 MeV = m*c^2. And the pairs actually will not have high kinetic energy, if created at threshold, basically since they arise from "tunneling." [I happen to have found 3 different published papers which state 3 mutually disagreeing formulas for the Schwinger creation rate, and I suspect all 3 wrong... but they all agree it is nonzero :)... ]