Not sure if folks are looking for an answer on this still or not, but I went through many pages of possible solutions. In the end, what worked for me and got my Instagram account "unlocked" was restoring my iPhone, by using the "Restore" option in ITunes. Remember this brings your phone back to factory, out of the box settings.
It wasn't a huge deal for me because I didn't have alot of apps I need to re-download, but I can testify that it did work. Just do NOT use the "Restore from Backup" option as that will just put the "bad code" back on your phone.
It took about 30 mins or so, after it was all done, I re-downloaded Instagram and POOF, I'm logged back in. Just have to go through the hassle of re-doing all your settings.
Oh and if you're on Verizon, grab the app "Backup Assistant" before you do this, it will back up all your contacts only, this saved me ALOT of work! You just download it again after the restore and it will guide you through getting your contacts back.
Hope this helps!!