I want to mention, I never considered anyone using the Running Martingale would also be using ANY kind of curb device, bit or hack on that horse!! Silly me, I thought all those using Running Martingales would be using some kind of ring sided, direct-pull bit on the horse.
A correctly adjusted Standing Martingale or Tie-Down, will allow a horse to easily use his head, yet not get it up above the safe level. Should be usable, not interfere with the snaffle type bits, ring-sided or any curb bits, Mechanical Hackamores.
I mentioned the water crossings, removing long strap for that, because there was a man and horse killed when he went into a lake, fell over the drop-off on horse with a tie-down. Horse sank like a stone, couldn’t get his head up, man could not swim, 20ft out into lake. Man was in a horse forbidden area, to take horse into water, ignored the sign. Swimming horses ALWAYS raise their heads. Even the running martingale would be dangerous, every rein pull puts nostrils down, if swimming water. Restrained heads on horses who will be in deep or unknown water are DANGEROUS.
I guess if I was as worried about control as some folks (rightly so!) are, then I would go on to the Mechanical Hackamore. You have enough leverage to help stop him, could add the tie-down to keep head under a certain height for your head safety. You can still pull and circle, keep control. No mouth pressure on horse, easier on you as well. LEVERAGE is your friend if horse brains comes unscrewed because of his surroundings. Yep it does happen, horse has to acclimate somehow. Nothing you can really practice at home for. Takes repeated exposure, rider keeping control gently as possible, letting horse see stuff, working thru the steps as they arise. Yet if things get “kinda Western”, the curb leverage control should still be there to keep YOU safe, steering horse around, maybe circling, to regain his mind.
I REALLY would not want to deal with your horse problems using the ring snaffles and running martingales. You can always back up to less strong measures, AFTER horse is more reliable. Many kinds of comfortable hackamores, that will keep you in control if horse never is 99.99% reliable.