Thanks for bringing this up, and you're right that this is closer. I still think it's imperfect, because a gig economy worker who works 35+ hours per week would be considered "employed full time" (footnotes, https://www.bls.gov/cps/cpsaat36.htm) and as far as I know would not be included in the U-6.
I don't have a more recent statistic, but in 2018 half of Uber rides were provided by drivers working 35+ hours per week: https://www.epi.org/publication/uber-and-the-labor-market-ub...
So while I was perhaps too harsh on the work of the BLS, I do think that newer metrics are warranted.