I don't think that cap on the carb will feed the carb very well. It DOES reduce air flow. And can mess with the carb fuel draw. And cause lean conditions.
Air cleaners are designed with a curve in the bottom plate, and it sits lower than the carb throat so that the air feeds into them as a smooth flow all the way around the carb and promotes good even fuel draw.
If you put the original air cleaned back on the car and feed it with your temp reducing fresh air duct you will be in the pink.
Your carb cap is for forced induction.
A bit of a long post, bear with me.
At first I couldn't find an air cleaner to fit the Carter AVS carburetor neck, since I moved from a 2 barrel carb to a 4 barrel.
But all of your points are valid for sure, I'm not discounting that thought.
From my limited knowledge, wouldn't the ducting enrichen the A/F mix?
Due to the engine taking in air "through a straw" so to speak.
The smooth ducting should reduce turbulence and add some sort of "ram air supercharger effect" albeit a negligible amount.
one other thing I thought was the ducting creating some sort of a tuned runner length sort of like the cross ram manifolds on 1962 Chrysler 300's/imperials.
This was mostly an experiment to see how it would work, a proof of concept perhaps?
Long runners increasing torque while short ram would be increasing top end performance, yay or nay?
The ducting is on a cruiser type of a lead sled, so it doesn't see much high RPM, which definitely the ducting would choke the engine, it's
More "optimized" for low end torque.
But that's all I got, just some theory I had while putting the ducting together.
Thanks for voicing your thoughts, it's good to hear some feedback on a pseudo project.