emmtee
That’s really promising that your endo has a go-to surgeon for thyroidectomies. When I was first diagnosed and considered TT, my endo presented me with all the treatment options, but I got the impression that not many patients in their practice chose TT. The surgeon she referred me to told me he wouldn’t do a TT on a Graves’ patient because the enlarged thyroid made the surgery more difficult. Fast-forward four years and I had a nodule, suspicious for cancer, that was actually larger than my thyroid, so there was no question that I needed surgery. Fortunately, the hospital had recently hired a highly experienced and respected endocrine surgeon. My TT went off without a hitch and the tumor was benign. 
With your labs, hopefully they’ll go by your T4 and T3 when they declare you euthyroid. Changes to TSH lag behind T4 and T3, and in some people (like me) they remain suppressed. Mine was still suppressed when I had my TT, as it had been for the last 3 years.