As far as the gear, you might look in to a "Little S" hackamore. That's what I use when my Nurtural isn't enough.
Also, you might take a look at what you're feeding him. Nutrition plays a BIG role in horse behavior. As does tack. A check by the saddle fitter and horse chiropractor might be in order. A teeth floating might be needed as well (can effect your bitless and definitely effects the bit).
Some more training is a good idea as well. Work with a Dressage instructor (not just an eventing trainer that does Dressage) on getting your horse to be more balanced and listening to your seat more. You should be able to use your seat and weight to slow your horse down without having to rely on your reins much.
Teaching the horse what "WHOA" means is a good idea as well. Those western trainers can teach you a thing or two as well
. When I say whoa, I mean "WHOA NOW". Not in 30 seconds, not even in 3 strides, but NOW! First work on the lead rope. Do not over-use the word. If he doesn't stop on the first "whoa", get big and send him backward, then jerk the rope and say "Whoa" again asking for the stop. Praise him heavily, including food treats if he's good with them, when he does stop on whoa, even if you had to back him. You want it to be very clear to him exactly what you want. Once he's doing well on the lead (leading him from BOTH sides!!), then move on to the lunge line or round pen. Once he's doing well in the round pen, then try using it undersaddle.
When teaching whoa, be sure you ONLY say whoa when you want and expect a FULL STOP. For just slowing down I say "Easy" or for a fidgeting horse I say "Quit That". Teaching the "Whoa" comes in VERY handy! I teach it and how to ground tie to all of my horses. I have the best behaved "English" horses my vet or farrier has ever come across, lol.