My question is, should I seek a second opinion and see if a different doctor would write up a statement that isn't a damning as the one this doctor did?

I'm not a doctor and I have not experience with pneumothorax.
If I were you, I would sign up for the best health insurance that I could find, then I would go see the best specialist in pneumothorax (the best specialist that I could find in my state that was also covered by my insurance), and I would get them to evaluate my condition, and see if there is anything that can be done to help avert another pneumothorax. In the process, you can get a 'second opinion' for the FAA. If you're seeing the 'top specialist', their (hopefully favorable) opinion will carry more weight with the FAA. Your first doctor might be a dud and you have nothing to lose (except money) by going to a second doctor. Have a copy of the x-ray sent to the second doctor before your appointment.