Yes, you would have to use that o ring for dressage, but for jumping is there any reason you can't go back to that kimberwicke?
The Myler combo you posted is an excellent bit IMO. It'll give you the added nose pressure as well as the little bit of gag, which will give him "warning" and allow him the option to respond to the poll and lip pressure before it fully engages with the leverage. The mouthpiece is very nice as well. Not nearly the same action however as the comfort snaffle posted.
I do disagree however with Puck about everything giving you more control than a loose ring single joint snaffle. Single joints are harsher than something with a lozenge, so it will take less, but I do agree that some horses do not like the nutcracker action of the mouthpiece. As well as that, when you pick up on a single jointed snaffle, as it pinches the tongue it will also press up on the palate. If he has a shallow palate, he won't like that at all and probably won't like ports either. Even with that though, a single jointed kimberwicke will do the same thing.
The comfort snaffle Puck posted as well is a wonderful, wonderful bit that I use often but you won't get any extra out of it than you have with the single jointed loose ring, unless he's running away with you because he hates the feeling of it...Which I highly doubt if he is fine with it in dressage.
I consider jumping horses on the same lines as the barrel horses I ride. It's something that is going to give them an adrenaline rush, and they will get stronger. A snaffle is not a fix-all, ride-in-all bit for horses like this. I always bit up to ride my barrel horses. You can ride light with more bit and have the extra if you need it, but if your horse is strong in a snaffle you'll have more yanking and pulling to do if you get into trouble and need to keep yourself safe. And trust me - Some horses will NOT listen to one when they learn how easy it is to pull through you, and there's nothing you can physically do to stop them sometimes.
Some other options, besides the myler combo and the kimberwicke:
Draw gag, I would not suggest this bit if your horse gets heavy on the forehand. Otherwise, it's great, and I use one often as well. That's just the image, you'll have to buy the cheekpieces and bit seperately I think. Nunn Finer Rope Gag Cheeks | Dover Saddlery
Either of these Ovation Elevator bits are excellent as well. The one with more rings gives you more leverage. Ovation Elite Center Oval 2-Ring Elevator Bit | Dover Saddlery Ovation Elite Center Oval 3-Ring Elevator Bit | Dover Saddlery