Hope it helps. We've actually done two different things to deal with the issues of fluency and anxiety.
Initially I had her do the page where I was secretly timing her. After three days of that, I showed her the times. She then did the practice for another couple of days knowing she was being timed until the time got down to where it needed to be.
That instance I think was 100% anxiety.
When she was memorizing the multiplication facts and she needed to memorize them instead of working them out each time, we dealt with the associated anxiety by just counting how many she could do in 5 minutes, making the goal of increasing the number in that time. It was an interesting process, where we'd see her drop WAY down (like by half) about once a week, only to be followed by jumping up 20% over where she's been previously the next day. Dealing with the anxiety and perfectionism was really tough on those days where she dropped way down. After we saw that happen a few times, though, we noted the pattern, then I'd start to celebrate the big dips, saying "Wow, tomorrow's going to be AWESOME." We made several assertions that this must be some sort of rewiring leading to this effect.
As someone around her was saying recently: Brains are weird.