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The math is actually simpler than what you proposed. Z-Spread is always computed as the parallel shift in a zero curve required so as to reprice the cash flows to a bond's cash flows; i.e., you solve for the $s$ in $$P + AI = \sum_{i=1}^N c_i \cdot d(t_i) \cdot e^{-t_i \times s}$$ In the multi-curve world, you simply compute both the LIBOR OAS and OIS OAS ...
if you let the implied vol depend on K you get two terms the first is $N(d_2)$ but you get a correction term which is the slope times the vega $$\frac{\partial C}{\partial \sigma} \frac{\partial \sigma}{\partial K}.$$ (see eg my book)