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I did some research about the high frequency ringing and determined that it was due to the parasitic inductance and capacitance in the wires/FET etc... The frequency is around 3.3 MHz, so I think this is reasonable.
Anyway, I also read about RCD snubbers and hacked one together out of components laying around. It's pretty ugly, so I didn't even take a picture of it. But it took care of the high frequency oscillations, but left the high voltage spike.
The first picture shows the new readout at low power, and the 2nd at high power. The high frequency oscillation is damped away, but the voltage spike remains.
The last photo is actually taken while charging a battery at 20 amps (I used the 12V SLA accessory battery from my EV as a guinea pig). The FET was starting to get warm, but still touchable, but I didn't let it go long since I didn't want to push it.
So, given that my purpose of this stage was to demo the basic power circuit by actually charging a battery, I'd say this is a success so far!
Things to do:
Determine if the voltage spike is a risk. Will it increase at higher input and pack voltages? Is it only dependent on current? I plan to do some tests at 120V, but have to get my hands on an isolation transformer in order to use the scope (I tried - apparently it doesn't like grounding the scope to a rectified rail).
Get some more input caps. At 20 amps, they were draining to zero quickly on each AC cycle. I don't think this is good, but I really don't know.
Then, further into the future, implement a microcontroller to fully automate charging...
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