My horse has a lovely, forward walk and trot. However, his canter has always been sloppy and uncoordinated (...but I'm not sure what to do aid-wise when it comes to a horse being unbalanced and uncollected. What can I do to fix it?
Unbalanced means he does NOT have the muscle to hold the canter (hence why he can start OK and end up running, 4 beating, etc...uncoordinated). So for a while to help him learn to balance with a rider at the canter:
1.) Lunge him in side reins, asking for canter from trot. Do NOT let him stay in canter more than 1/2 a circle (5-6 strides) before asking for a trot. Repeat trot/canter/trot transition several times. Be certain you give him the opportunity to stretch his head down (side reins NOT hooked) every 10 minutes or so to help prevent his back from getting too sore.
2.) Once you can lunge him with side reins and he can maintain a nice canter twice around a circle without a rider then repeat the 5-6 strides of canter with LOTS of trot - canter - trot transitions with a rider on his back. The key here is for the rider to ask for the trot BEFORE the canter gets bad.
When riding the rider MUST allow for lots of "Long and Low" during the ride so the horse can stretch his back muscles to prevent them from getting sore and cramped. If they get sore his canter will get worse, not better.
After doing the two steps above come back in 3 months and let us know how much better the canter is. You may have some new issues to work on then.
And the key to transitions is they MUST be good transitions - do NOT "chase" the horse into the canter from the trot, nor yank on the horses mouth to get a trot when you're cantering. Transitions must be smooth and the rider help the horse balance with a nice outside rein connections at all times - especially during the upward/downward transition.
By good rein connection I mean - not too hard (bone crushing) nor too soft (like a dead fish - limp).