> This is one area where the left-right paradigm breaks down
No, it isn't.
> I've see far more leftist war-mongering in the last decade than anything coming from the right
That's probably because you have confused as “left-wing” the center-right neoliberal faction that's been completely dominant in the Democratic Party since the early 1990s (though in the last couple years that dominance is weakening and there’s a real chance that they won't have someone from their faction secure the Democratic Presidential nomination next year, which would be the first time since at least 1992 that that has occurred; 2016 was the first time since at least then that there was even a significant contender that wasn't from that faction.)
> If you imagine the quintessential American man, a hard-working White lower-middle-class family man, it's impossible to assign to him modern leftist politics
Odd, then, that that's exactly the group in which the actual left-wing challenger far out-performed the center-right establishment candidate in last year's Democratic primary (and, also, during the primary when the two were placed in general election polls, the same effect was seen.)
Modern left-wing politics do just fine with the working class, including the white male segment of the working class. Center-right neoliberal capitalist politics and the bourgeois minority identity politics that faction engages in to divide the working class and obstruct the formation of a working-class identity, don't work for the white working class (and aren't intended to) just as the white nationalist identity politics embraced by the other party’s capitalists for the same purpose don't work, and aren't intended to, for the minority groups to whom the Democratic center-right’s identity politics are targeted.