Will Lingual Braces Correct TMJ and an Open Bite? (photo)

I have TMJ and an open bite. The orthodontist is suggesting to remove 4 molars (1, 16, 17, 32) and getting 8 TADs (Lingual and Buccal 2, 3, 14, 15), along with braces, to fix my problems. There is nothing wrong with my molars, are the extractions necessary? Also, I am considering lingual braces. Will lingual braces be a better option than traditional braces? the cost will be almost 10K! is that a competitive cost?

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