Well, here are my 2 cents...
First of all, rubber sounds lovely, in concept it's the ideal thing to put on a bit - but it too has some downfalls. Rubber makes a bit much thicker, while realistically a very narrow bit is harsher, but an overly wide one can be very uncomfortable too. It also has a tendency to get chewed up, making little sharp edges that really hurt. My very small pony I just started with a bit (for driving) I started with a flexible rubber mullen mouth, but being so thick it was awfully uncomfortable for him, despite the 'tongue relief'. I switched him to a sweet iron french link and his problems were solved.
French links IMO, are the best bits to resort to when something isn't working. Medium thickness, no rubber, a sweet or warm metal (like sweet iron or copper) - all those things are ideal choices in a bit. French links, IMO, are more ideal than single jointed snaffles because you don't run the risk of the joint hitting the pallet of the horse - which often causes head tossing or leaning hard on the bit. Leaning seems to be your problem? When the single joint of the snaffle hits the horse's pallet, the horse will lean into the bit, pushing all the pressure on his bars and tongue, maybe opening his mouth if there is no noseband to prevent that, all to get the pressure off his pallet. So perhaps, when you ask him to stop or turn the bit is actually bothering him and the easiest way to avoid the discomfort is to push into the bit further.
If he's not stopping with the pull of the reins (of course backed up with seat cues) you have 2 things to look at and fix, a bit he doesn't like and more importantly his training! So first I'd switch to a milder bit then I'd go back to training.
I'd hop on and ride this horse through a million transitions and changing figures. The more you ask of your horse, the more he needs to pay attention. Always remember "Ask Tell Commad" - Ask the horse with the gentlest cue, if no response, tell slightly stronger, still nothing COMMAND it - After a few good rides where you ride through lots of gait changes and flat figures you'll notice you're needing to command or even tell much less often. This teaches the horse to focus on you and try to feel the pre-cues to avoid the stronger cues. Remember to always look where your going and use your entire body to ride the horse, not just your hands. Eventually you'll just look where you want to go and he'll be going there.
If he gets hyped up over jumps take him back to flat work and gradually reintroduce jumping in a more controlled manner - at this point if you can't stop or steer easily, he shouldn't be jumping.
ETA: Mullen Mouths are also wonderful bits and will prevent the same issues that french links do.
Last edited by PunksTank; 04-04-2013 at 10:31 AM.