Just a couple comments om the videos and the findings. In the first video your power supply shows 5.5v being input into the 5v regulator in the circuit. Typically, those regulators need 1.2v more than their output voltage to function properly. I would expect that you were only getting 4.3v out of the regulator to run the circuit - probably the barest minimum it would run on and why you were running 5.5v instead of 5v as you stated in the video. If you had set your supply to > 6.3v (7.5v is the minimum recommended voltage), the circuit would have been much happier.
Second, i noticed that your scope probe is not grounded and nothing is connected to the ground lug at the lower right of your scope. The waveforms you got were decidedly noisy due to this. If you had clipped the probe's ground wire onto the board ground your waveforms would have been much cleaner.
I was more concerned with the voltage you were running it with. The mosfet uses the unregulated input voltage to generate the HV, so it was switching 5.5v instead of 7.5v or 9v. That would make it run a rather high duty cycle in order to generate the HV. I think the Atmega should work down to around 2v, but the K155ID1 probably needs 5v +-10% to function properly.
Ian recommends a power supply of 7.5v to 12v @ 1a to run the project. I have been running the ones I've built on 9v supplies I bought from Ebay or Amazon, I can't remember. Ty says his were not reliable on 9v supplies so he uses 12v. Whatever you choose, make sure its at least 7.5v @ 1a. The wall warts are pretty cheap and readily available
Yeah, I've since kicked everything up to 9V 1A since I have a bunch of those wall warts laying around for various Arduino projects and it's running things fine now. If you've noticed, only in the first video was I running things at that low of a voltage. Since then everything has been run at 9V. But, I don't think that the Atmega would have been killed by running it at 5.5. So, why it was killed is still a mystery to me. If I get really bored, I might dig into it deeper to see, but for now the spare is working just fine and the clock is running, well, like a clock.
Thanks for clearing up the mysterious waveforms. I kind of suspected it was noise but wanted to be sure.
I've killed a few Atmegas in my day but not many - they seem like they are pretty sturdy. I see you're feeding power in through the barrel connector so we can rule out accidentally putting power input onto the wrong header pin. The board has a reverse polarity protection diode - if connected with reversed polarity it simply wouldn't turn on. So I guess what I'm saying is... I have no idea what happened.
Look into it later when the dust is clearing off the crater.