Update: Got a fair bit further, even fought some champions.
Higher threat forces put up a stronger fight - but that's just it, it's a *stronger* fight. I was able to defeat most threats - 12 cop squad, champion, 25 cop squad, 4 champion party. I suspect the 16 champions is way too much to deal with but anyone sane would have jumped by now.
In each case, it seems the correct answer to the problem is overwhelming force. More violence, more simply. Where I've made a tactical error it's in trying any plan other than 'get a big stack and throw it at them' (also, use tasers on the highest combat targets and then go down the list of best matchups).
Admittedly, I've got lucky and haven't had to fight a 20+ combat champion. Admittedly, I struggle to think of a way to deal with a hostile champion other than violence. Investigator, sure, but hostile out the door?
And if you're not actively trying to take the hardest fights, you can just... not. Champion detection resets on jump, I don't know if their 'aggro' also does, but it seems most likely. In this case, you can avoid taking any fights you don't need to, and in *that* case...
Yeah, sudden violence is just easier than doing anything else. There are other options, but they seem best used mainly to set up for the sudden violence.
I'm not sure how to... solve... this? On one level it makes sense. The simplicity of the combat system isn't a problem, necessarily, but it does get a bit frustrating that complexity is counterproductive.