I'm not sure what would be the point of doing that because there is no guarantee that they will see or accept your other lab results. It's better to work with, not in parallel with or counter to, your doctor or care team. It may take some research, persistence and persuasion on your part, but that is how you build a team...

This is what I might say -
"Good morning, doctor, I am part of a Bronchiectasis and MAC Support Group through Mayo Connect. This is very helpful to me because [choose one or more...MAC is so rare I never heard of it before my diagnosis, I don't know anyone else with this infection, I don't know how many cases you see every year...] On Connect, I communicate with hundreds of MAC patients across the country and even in other countries. Many of them are able to get very detailed information about their NTM from sputum samples, including species differentiation, colony counts and medications sensitivities. I would like for US to have the same information when WE make decisions about MY treatment. Can we find a lab, here in Texas, where you can send my samples for processing? Or, if there isn't one, I have done some research and found that National Jewish Health (NJH) in Colorado does this detailed testing and accepts outside specimens on request. There may be other labs that do this as well."

This would tell your doc you want to be an active participant, open a conversation between you, and maybe be the final "push" for you to find someone new if they are not receptive.
What do you think of an approach like this, either in person, on the phone, or through your patient portal?
Sue
PS. I may have been "fired" by a doc a few years ago when I tried to get help on my own, and they took great umbrage.