Speed as a result of good bodywork is a different topic. It starts with learning to take slack out of the body. Once this is achieved any action is more immediate....Slack is very interesting to watch in people as they try to move and react. It not only accounts for slowness it also bleeds energy when we move and incrementally diminishes power transfer into a target and or how we receive power.
This is why I thought you would find Feldenkrais interesting. It's all about accurate sensing of slackness--though most people would say (it's easier to say) excess tension.
The fact is, slack is usually caused when one is using the wrong muscles to perform a function and the muscle that should be performing that function is left out altogether.
Feldenkrais excercises put the body in unusual positions, then demand a relatively simple movement that can only be done if one is using the correct muscles in the correct ways. Almost anyone will find areas where they're not using the proper muscles and so, in those unusual positions, they will find that certain simple movements are very hard to make.
After several repetitions, they invariably recognize the small error and sense how to activate that formerly "slack" muscle.
At the same time, they have to recognize that they have been unnecessarily using other muscles, resulting in unnecessary tension, which they can release as soon as they recognize it and begin using the correct muscles.
So the experience leads to awareness, which leads to release of both improper slackness and unnecessary tension.
The result is both freer movement, more spontaneous and immediate movement and a sense of more energy and less burden.
This, of course, goes back to the idea of "intent". Does someone "intend" to use the wrong muscles to perform certain acts? Does he "intend" to leave inactive the very muscles he should be using?
Of course not. And when he becomes aware of what he is actually doing, he also tends to recognize "why" he has been doing it that way, which gets into the realm of psychology and personality.
So the change is deep-reaching and, once felt, easily maintained and expanded on.
So that's why I think you would find the Feldenkrais Method both interesting and useful. It's all about intent and the use of the total body organism.