I went with S/S back in ’98 but as you say not doing that trip now (It was good!). Also Rocky Mountain in ’04 but they also stopped a few years ago.
I can’t think of any UK companies currently but Western Spirit mentioned in article have a good rep. Also Kaibab who are Moab based – I have done shuttles with them.
DIY is really easy, done it a couple of times. Fly into Denver or Salt Lake City, pick up a car and go where you want. All the places have plenty of route guides, you can do shuttles in Moab to get out of town and camp sites or accommodation to suit all pockets.
I have done them on my own and met others out there (including a STW’er). People are really friendly and of course no language issues. I should add though that I am happy on my own, would not suit everybody.