U-6 mostly comes from the BLS Occupational Employment Survey.
I don't think the original poster would be considered as part of U-6 unless his new job is defined as "marginally attached to the workforce or part-time for economic reasons." Simply getting a job with less pay doesn't put you in U-6.
If that's true, you've identified a huge hole in the measures. And you can't fix what you can't measure. I think you're right, because despite massive tech unemployment in the last 4 years, I don't see any of the charts spiking. Furthermore, people keep saying "this is captured in Figure X" but if it were really captured, it would be somewhat separable and could produce a chart that shows it in detail. I fear we're giving the Fed too much credit here.
I don't think the original poster would be considered as part of U-6 unless his new job is defined as "marginally attached to the workforce or part-time for economic reasons." Simply getting a job with less pay doesn't put you in U-6.