I love your vector calculus derivations. You certainly know how to wield these tools!
In my earlier posts I used the principle that the emf is equal to the rate of change of flux linking the loop. [The nice thing about this it that it works for both the cases of a circuit moving in a magnetic field (when the charge carriers in the circuit experience a magnetic force q(vxB) and for a stationary circuit sitting in a changing B, when the charge carriers experience an electric force qE.] In the case of a circuit translating in a uniform field, the flux linked with the circuit never changes (if you like, new lines of flux replace old lines), so the emf is zero.
It is, of course possible to show the equivalence of the emf line integrals in both cases (moving circuit and stationary circuit+changing B) to d[itex]\Phi[/itex]/dt. I used to be able to do it without looking it up!