Huh, why are C1 (in the first circuit) and V3 referenced to ground? (Doesn't matter in SPICE, but a real, noisy source will mind.)
Also, does it have to be a high side driver? Either way, your flyback signal is still beyond the rails, but it can help save on level shifting or N/P transformations (and in turn, confusions like C1 and V3).
Regarding stability, exact results depend on a lot of variables: the amp's response, the transistor capacitance, even the load's inductivity (which is probably a combination of distributed capacitance and lossy inductance). If you can't test your SPICE models against the real parts to prove them, then you're better off setting up a general enough circuit that can be compensated on the bench by changing parts values. (To that end, about all you'd need here is a resistor in series with C2, for a pole-zero compensator.)
You may also need/want some R+C across the output transistor, either D-S or D-G. This adds some capacitance in parallel with the transistor's own capacitance, but makes it lossy, tending to dampen oscillation. Specifically, lossy at the crossover frequency (which is in turn set by Z_load and Coss, and opamp GBW and compensation), so the exact value of R and C depend on the loop response. Downside: the output impedance is affected, so that it has a more resistive characteristic towards the cutoff frequency.
Ultimately, this limits the bandwidth of the signal you're looking for. This is inevitable: you can do better or worse with various circuits, and component choice, but you can't have -- and wouldn't want -- something with infinite bandwidth.
More generally, you may consider a circuit that's not trying to be an ideal impedance, but just starts out as whatever in the first place, and your signal is measured as a ratio of voltages or currents or impedances. An impedance bridge, for example.
Tim