I agree with Ben... Ipad Rehab is one of the best in the industry. However, it's an Iphone 6? Repair may not be the best option unless you are mainly interested in Data Recovery for personal reasons. Repair cost would equal the value of purchasing a good, used device :)
I recently had the same issue on a near new Iphone 6. I put it on a "Hot Plate" for screen separation for a couple minutes at 80C to soften the glue/tape to open it easily when I noticed it bypassed the error and I was able to restore it. However, after loading it with my account info to set it up and test it...it worked great! I was so excited!! So I removed my Icloud, deleted fingerprint, passcode, etc...defaulted it and it went right back to the error! So... I threw it up on the hotplate, heated a couple minutes at 80C and Walla! It worked again. I went through this about 5 times and think the Nand may have been the issue... I didn't get it to "Reflow" at such low heat, but made it expand (With Heat) enough for it to make a connection. I never reflowed or reballed it... I just sold it as a parts phone as I have several 6 logic donor boards.
But just for giggles...try to get it heated up with a blow dryer or heat gun a "Little bit" and try to restore again while hot and see if that gets it done... Just curious :) Good Luck!