Jake,
Have you ever done your Kata's while physically exhausted?
For example, Wrestle with two or three folks whose job is NOT to lock you up or submit you, but rather their job is to make you work against their body weight, to force you to always be moving and to deny you your strength. This can be a quite invigorating exercise/drill. One 'little' side effect is it teaches your body how to work when strength alone is not enough.
I agree. Even just extreme physical workout, such as jumping rope until exhausted, can have a positive effect on relaxation, I have found. Get to the point where you are so tired, you just don't care what your kata looks like anymore. You're too tired to even try to do it right. Paradoxically, you may find you do it right at that point.
It seems to me that there are some folks who are just naturally relaxed and some who are not. I am one of those who is just so lazy that relaxation is more-or-less my natural state. I don't recall having to work on 'being relaxed' in general (I have a host of other problems, just not that one).
Anyone who has ever golfed, played tennis, or played baseball knows that you cannot hit the ball effectively if you are tense. Good form depends upon relaxation. Trying to murder the ball (for me) always results in a big swing and a miss or a very bad hit.
Get tired. Wear yourself out. Let your body go limp, to the point where you can barely stand. Let the shoulders slump, fingers open, head rolling around. Think about relaxing each and every joint in your body, from your head to your ankles, individually and consciously.
Walk through your kata without punches, blocks, or kicks. Just walk the pattern, make the turns. Let your arms hang loose. You're like a floppy mess. Just let it happen. Breathe.
When you feel comfortable with that, add some punches and blocks. Make them weak and ineffective on purpose. Just flop them out there. Do that for awhile.
Slowly increase the speed and eventually the power. Try to keep in mind what it feels like to just slop through it; that's relaxed, that's loose. It's just too loose, but that's OK, you need to inform your body what it feels like.
When all is said and done, I will tell you this - a relaxed punch with proper focus will knock you down, howling in pain. A strong punch from a tensed up individual is not even close to being that painful. Just my experience. I have experienced this giving as well as receiving. I've gotten a soft slapping movement on my chest or arms that made me think I was going to cry. No punch ever hurt that much. There is much advantage to proper relaxation if you can embrace that.