The relaxed version should be more powerful than the tension filled version, just FYI. Can take a long time to get there.You hit it right on the noggin. I always warm up with a "relaxed" version of my kata but it comes out looking weak. I'll try that exercise + consider what Simon mentioned (I've never actually had a massage).
I've asked him on countless occasions and gotten quite in-depth answers but even targeting these problems has caused minor improvements at best.
And massages definitely help. Back when I was fencing, one of my friends had an issue where he could not release his tension. Before matches, I'd give him a back massage, and he'd do immensely better.