Reality Check = FAIL!
The first important consideration for this kind of breathing system, the conchoid lung, I believe, will be dead space.
The other important consideration is that your system isn't set up and doesn't function like a bird's respiratory system.
So, what will happen? --- Dead space is the term for air that sits in a tube that can not be properly inhaled or exhaled. In other words, your chest cavity is only able to expand so much, so the amount of air inhaled is limited by the available chest volume. The more tubing you add to the system, the harder it will be to bring fresh air in and clear stale air. The air that gets into the very end of the lung will become stale and will be unlikely to clear.
In a human lung, the entire volume is taken up by increasingly smaller branches and then even tinier ones. So, the large trachea divides into two primary bronchi each of which divides further into a couple more levels of smaller secondary & tertiary bronchi. These in turn divide into many bronchioles which terminate in alveolar sacs where gas exchange happens. This works well because the distance from any one alveolus to the outside is relatively short and the respiratory cycle can fill and empty the lungs without (much) air remaining inside (there will always be some).
Your conchoidal lung basically presents us with a very long tube. The distance from the most proximal alveoli to the outside will be comparable to the distance of the alveoli in the upper lobes of the human lungs. However, the distance from the most distal alveoli to the outside might be a metre or more! That part of the lungs will be filled with dead air that will hardly ever be cleared.
You'll have to either scrap the conchoid lung or else scrap the relatively humanoid thoracic cavity you described. See below under reinventing the wheel.
Bird breathing is complex! --- Birds have two lungs, nine air sacs, and a four stroke respiratory cycle. Inspiration brings 1. the current breath's fresh air from outside into the posterior sacs and also 3. the previous breath's stale air from the lungs into the anterior air sacs. Exhalation pushes 2. the current breath's fresh air from the posterior sacs and into the lungs and also 4. pushes stale air from the previous breath back to the outside. The result is a continuous flow of air through the lungs.
The extra tubing coming off the distal ends of the conchoid lungs will not effect continuous breathing. In stead, they will just create more dead space.
Conclusion. --- As it stands, I think your system will both fail to produce a superior volume of air flow & gas exchange and also will defeat itself by taking up too much valuable space within the chest with extra tissue and dead space.
Lastly, if you just connect those extra tubes to air sacs, well, then all you've really done is reinvent the wheel that avian dinosaurs invented millions of years ago. The argument for increased surface area for gas exchange fails again. Whereas before, only the most proximal portions of the lungs would really receive fresh air; now, only the most distal parts of the lungs will receive fresh air. Much of the lung's coiled up length will just have stale air passing through it.
I think diminished returns on investment will eventually lead to smaller, more straight forward lungs.