That's true of oat and rice milk, but not of almond or soy. That's to be expected: the former two are made out of starchy grains, the latter two out of fatty nuts/pulses. Those are on a par with milk for glycemic index (~25).

The worst case ("obese cows on a grain fed diet in a feedlot") is also the common case: if you go to the grocery store and buy generic "milk", that's what you're going to get. Organic may be slightly better, though it's unclear. You can go out of your way to get more sustainably-produced milk, but you're going to pay at least twice as much for it.

That's a decent choice, though I'd be happier if it were easier to verify. (I don't trust the labeling of "grass fed milk", and locally-sourced milk that I can check myself is hard to come by.) The small comfort is that dairy cattle have to be treated relatively well, since they can't produce good milk if they're sick or abused.