I have never experienced flickering from the aperture as is settles in place, although I can see why this would happen. I don't think I have ever experienced this is because my camera, the D3100, being entry level (and becoming a little under-featured for me) has a slow burst rate of 3 frames per second. Since the entire mechanism is considerably slow this would allow some time for the aperture blades to settle before the sensor gets exposed.
Yes, perhaps it is a case of "budget is better" for this particular application. That's one problem with these entry level cameras. They have just enough features to entice you in, but if you get serious about it, you rapidly outgrow them and you end up with a second body that you can't sell and will probably never use again, heh.
Watching the video again, I can see a little flicker in the f/22 sequence, but not much, certainly not as much as I've experienced with some lenses, so still very impressive. It might be the slower framerate that's making it less obvious too.
If your camera has a quiet mode, I suggest that you try taking time lapses with that and see if the flickering improves. This may include a delay between closing the aperture and opining the shutter.
The problem with quite mode is that I'm using an external intervalometer to control the exposure (shutter speed) for bulb ramping. So, using quiet mode and having that delay throws all the calculations off, and getting the timing ms perfect to cover that initial delay can be tricky.
But, even using the built in interval timer, using either the quiet mode or the delay feature which locks up the mirror before the shot, flicker can (and often does) happen. Try some other lenses, it might be that the lens & body combo you're using is particularly well suited to this kind of task, so you haven't noticed it yet. I have a Sigma 10-20mm f/4-5.6, which is an absolutely fantastic lens, but doing beach cloud scenes it flickers like crazy once you get down to f/8-f/16 and you're playing it back at 24fps - Fortunately I have the B+W 10 stop ND filter, some rather sexy Schneider 4x5.65" ND filters and the Z-Pro holder so I can shoot it wide open (where the Sigma performs beautifully) and still lose up to 20 stops of light if need be (very nice for those long exposures with the sun in the shot).
This is one I shot on the Sigma that wasn't too bad (although Youtube's compression gives it horrible moiré and artifacting issues).
With the M42 lenses, there's no workarounds needed. I put them on my D200 & D300s bodies using an M42->Nikon adapter with a diopter to retain infinity focus, and the aperture never changes (because the camera isn't setting it each time it takes a shot, it's controlled on the lens itself and stays constant throughout). Because most of them are 30-40 years old or more, and quality control was pretty much absent from their production, they can have some great character too.