After reading this thread I fell into a youtube hole of tele-based jazz players like Ted Greene, Tim Lerch, and Julian Lage, thinking about the whole technique vs tool dichotomy. Two things were regularly discussed: heavier strings (though not necessarily flatwounds) and playing with a lighter touch overall. I think it was in a Tim Lerch video he says that "amplifiers allow players to play quieter", which sounds so counter-intuitive to how we often talk about electric guitar but really hits the nail on the head. Turn up the amp, but turn down the guitar (if it doesn't have a treble bleed) and play softer. I think I ran across a Metheny clip in which he says roughly the same: guitarists who only play the guitar on ten and pluck relatively hard don't quite get that tone. (side note: take that Beato and your "9's sound the same as other gauges")