Adding a touch of bulk local capacitance dramatically improved the Peltier power supply’s transient performance when the MOSFET turns on:

That’s a 33 uF 300 V electrolytic that started life as a surface-mount kludge, simply soldered to the Peltier supply’s screw terminal pins on the bottom of the board.
With the cap in place, the supply drops to 4 V at turn-on and bumps to 6 V at turn-off, with the transients much better-behaved now.
Those spikes at the turn-off transient are also somewhat better, even if the MOSFET drain rings for another cycle before dying out. The peak is down to 35 V, which I think comes from the other end of the circuit being more reluctant to instantly jump 70 V, and the width has decreased, too:

The ringing jumped to 15 MHz, rather than 5 MHz, which means it’s over faster even if there’s another cycle. If it were any worse, I’d be forced to re-figure the snubber RC numbers…
The Miller capacitance effect still shows up clearly on the gate drive in the lower trace. There’s a reason why you really need higher-performance drivers for faster circuits!