Your references to the TSA and the FAA , along with your spelling of 'fibers', make it clear that you're in the USA. This website is based in the UK, where rules upon the wearing of face coverings (which is the actual term used in our own legislation, rather than 'face masks', per se) might be slightly different.
However the TSA's website, referring to the relevant CDC order, states this:
"According to the CDC Order, face masks should cover the nose and mouth and fit snugly against the sides without gaps. Masks can be either manufactured or homemade and should be a solid piece of material without slits, exhalation valves, or punctures. While medical masks and N-95 respirators fulfill CDC and TSA’s requirements, face shields and/or goggles are not an acceptable substitute for the use of a mask; however, they may be used in addition to an acceptable mask".
So, when considering any adjustments of your own to regular mask-wearing, you need to ensure that you comply with those requirements throughout your journey.
I can't really see what you're making such a fuss about anyway. Here in the UK, we have to wear face coverings on all public transports, as well as in shops. In many other countries the rules are far stricter. For example, it's essential to wear a face mask at all times in the street in Italy. My Italian friend briefly removed his and got slapped with a €400 (= $450) fine.