With my method I do multiple tests, this means I do not risk getting the fastest time the meter can do.
Looking at a couple of meter and seeing which is fastest may be more interesting for some, I like the numbers because I can compare all the meters I have tested (>100). If you measure frames you can, of course, do the same, except for continuity.
I used a frequency counter, tied to the arb that would output a 1kHz clock once triggered. The counter is cleared on start and counts up while with a 1mS resolution. The load is applied or removed at the trigger time. The camera has just shy of a 1000fps sample rate. With this setup, I can get some decent numbers if it were needed. I can run up to three meters this way in parallel and it makes no difference as far as the absolute data that could be collected. I'm looking at what was captured with the camera is all. The fact we can see the meters side by side real time is just an added plus.
The downside to this method is my camera can only capture in bursts of two seconds. I currently trigger the camera using the same trigger. Some meters take longer than this to settle. In these cases, I have used the cameras manual post trigger to capture the data. A pain. I had written the guy who designed that high speed camera when he announced the prototypes and offered to buy one. That camera would have been a big help with the testing. He gave them away as part of a promo. Dave did a review of the one that was sent him.
I understand you want numbers and are your not using the scope to get them. I understand your jig, tied to the arb but I am not understanding how you make this precise measurement. Could you please explain how you actually get the settling time?
I did not bother checking capacity before I had the AC switch, only disconnecting one way may lead to errors (I have no idea if it do, I have never bother comparing).
So you haven't checked if there was actually a problem with the single FET. More just trying to prevent a possible problem. Makes sense. Adding a capacitor may be of interest but I would like to go down to 200pF ish and up around 1000uF as most of the meters I have looked where slowest at the two extremes.