It's got nothing to do with being on your feet, and all to do with the fact that you're tall and having to bend down to reach the table. You might not be bending much, but it will be almost continuous. I'm a short arse, but I've got a back injury which reacts in exactly the same way- I'm about 5'7", if the wind is in the right direction, and even just emptying my figurecase can cripple me.
You need to either lower yourself, or raise the playing surface. Most of the places I've been to have tables that are ridiculously low- I used to work in a hospital (which is where I wrecked my back, so maybe it's not the greatest example!), and the level at which a table-top is comfortable and safe to work at is a lot higher than anyone would realise. So, you either have to sit down, or raise the table. Stretches will help a bit, but it's going to take a concious effort to make sure that you improve your posture as well, making sure that, after every move, you stand tall and with a straight back. Doing that will help a lot more than a mat under your feet. Hope it feels better!