I don't know if tads meant you can't wear lingual braces. I thought you couldn't wear lingual braces for jaw surgery.
I saw someone who had a small upper jaw impaction with about as much gummy show as yours and I think her tooth show was acceptable after.
The choice is yours in the end, but I'm just making you aware.
Surgery always has risks. I was deprived of informed consent and there are deformities in my face caused by the surgery that I cannot find one successful reparation case of. It always fails.
You can always get SG if tads fix your bite, and I cringe saying that because I don't recommend SG. After the jaw surgery I also constantly have hemifacial cheek spasms
As for TADs, it's best to consult with numerous orthos. The ones I saw said it may not work, but there are drastically successful cases online now, where yes, their profile was improved.
I don't know if the distance between your nose and mouth will look different. The soft tissue will stay the same and may or may not look bigger if the upper jaw is advanced, but that's something u have to research on your own.