for the quarters in - try leg yielding on a circle, spiral in and out. Better try at trot first though, and canter should be spiral in, leg yield out.
Try shallow loops along the long side in canter. Start with just a meter or so an increase to, say, 3 m. If this is fine, you could build up to a little counter canter
If he is Quarters In at canter, could there be something there to explain the walk as well ? i.e. some stiffness or muscle weakness that you need to work on ? Even if only small.
I would try lots of suppling exercises at a workman-like walk. Don't try and shorten the reins much at all, i.e. shorten them to just before you get resistance. Again use the spiral exercise at walk. With some of these exercises you should find the horse naturally engages more and collects themself. Then you just take up whatever slack they create ! Lateral work - leg yield, forehand in (not quite a shoulder in) and so on, but all without shortening the rein, should also help.
if it isn't physical, the tension may relate to someone doing work like this before but using too much rein - so if you do as much as possible but all at "working walk", it might help.