the aluminium air nozzle its noticeably cooler than when it comes out of the nozzle itself.
Maybe opening the holes in the air-tube will help? It will reduce backpressure and thereby heat. Do you have a silicone sock around the heaterblock?
Chilled air is definitely a good idea, but adding a reservoir like an intercooler is not. It'll be OK if you run the pump at 100% all the time. But in many cases, the fan is PWM controlled by the slicer. A reservoir would cause a delay.
You could try to chill the air with a Peltier element, and cool that with a watercooled block.