I don't know if BTD is still in business. I placed an order and cannot get in touch with anyone in customer service. Less Wright's LinkedIn profile indicates he is employed at Facebook effective Jan 2022
I don't know any company off the top of my head that uses flux grown sapphire rough in general, although the hydrothermal method is similar in that it takes a lot longer to grow the rough.
Gary at Finewater gems and Gene at Precision gem have access to all kinds of lab grown rough, and they do precision custom faceting in many styles. They would be the best resources I can think of to contact about pulled vs. flux vs. hydrothermal.
I have a lovely royal blue asscher lab sapphire from Gary at Finewater, and it is a true, lovely royal blue. It goes a bit dark with less light of course, but all gemstones change a bit depending on lighting.