I don't think it's a good thing to stress the cities too much, especially the high-commerce ones. However, I'd also avoid working any food-negative cottages. City "whip plan" should be something like:
Mutal: no whip, just grow and max out base hammers
Lakhama: whip trebs/galleons 9-6, put OF in mostly jumbos. Better to 3whip when possible as it reduces unhappiness. Only regrow on food-neutral tiles (avoiding the hills village)
CI: whip trebs/galleons 9-6 into Globe
Uxmal should probably get an extra workshop + windmills and not be whipped, as the food surplus is extremely low and we're whipping away really good tiles
Mayapan: 2whip stuff (elephants and trebs) 8-6. No need to worry much about unhappiness here as food surplus is so low.
Calakmul: whip stuff 9-7, then Cannons 9-6. Whipping trebs 9-6 here would mean not working the iron tile for one turn each time, which will eventually be a big hammer loss. I think we can accept a bit more unhappiness and build a Ball Court with the "extra" hammers"
Oxhuzita: land not really improved yet. For now, just have to make sure that pigs + all GrassFarms are worked even after whiping. The stone should be whipped away and added back during growth. After RP the windmills will also be worth working.
Quirigua: whip 5-3 (work all 3 farms and add the copper mine at size 4)
Xukpi: whip 4-2 (work clams+upcoming windmill, and add upcoming WS at size 3)
Of course, this is more of a rough guideline than a very strict plan, but I think that it should get us where we want to go.
About banks: if we are to take out 2-3 AIs, I would build every bank I can in Mutal, Lakamha, Uxmal and Mayapan as long as it doesn't hamper war progress. But by the time we reach Rifling, the "new" cities should have reached cruise speed and production should be less of an issue, especially if they haven't got their own Rifles yet. In these cities, banks will pay for themselfes after ~8 turns of 0% slider. Considering that we'll likely spend 40+ turns at war and a few more not being able to hold a 100% slider, they will definitely be a big boost.
I'll be away next week btw.