Just for fun, let's try it with a mirroring output. In order to obtain this kind of coupled outputs, the taps of the Galois register must be the counterparts of the ones of the Fibonacci register.
The seed choice is not relevant since it would introduce only a shift in the output. In such a register, all possible states are visited - except the null state, which would make the register collapse in a sequence of 0s. The two types of LFSR produce the same result - minus a reflection and a translation - when the taps are the ones generating a maximally long LFSR.
