The power of AC should be equal to power used (=heat produced) by miners.
Without actually forcing hot air out, we talking (1250w*4)+ (3200w), which will require a very huge air-con system, which is a bad idea IMO.
Use a Y duct with an incline duct fan, and rest assured that the AC hole won't be large enough, the standard hole saw we use here is 6.5cm, you will need to widen it by a lot.
You are totally correct for default OCs, but he underclocks them really hard, it could be viable to use AC with a single hole (let's say 10cm
2) and small industrial fan.
For default OC or even overclocking above that, I would recommend some really good industrial fan with high m
3/h flow and good pressure. Avoiding AC is preferred as it adds additional cost to it as well.