A martingale probably will not cure this.
I had success with raising my hands so that the reins came up on the side of the horse’s head (be careful of the horse’s eyes!)
WARNING some horses will jig around and then DIVE their nose to the ground. This is fine, apply your legs and the head tends to come up some. DO NOT try to prevent the nose diving to the ground. Other horses tend to stick their noses out a little when they lower their head a little bit. Let these horses meet your soft, relaxed fingers with an advancing hand.
Repeat as needed, do it only when the horse is inverted. Try to keep a soft contact, letting the reins slip through your fingers is fine, and keep your fingers loose and inviting so the horse will enjoy your hand when he/she asks for contact.
Then you have to work on getting the horse’s back strong enough to carry the head at a normal height.
At one time I had a crazy mare who inverted due to past abuse with the bit, a balker/bolter who liked her face horizontal to the horizon. At first I had her in a double bridle (thick curb bit) and standing martingale while I raised my hands, keeping a soft contact with the bradoon until she moved her head down and nose out, then I continued on contact. She improved somewhat but not completely. After about 5 months of this I lunged her in a Chambon three times and within a month I got her to where I rode her in a snaffle with no martingale or noseband.
A few years later I discovered she preferred a Cambridge mouth ported Kimberwick, I had finally found a 4 1/2" one and most of her remaining mouth problems went away.
An independent seat, soft relaxed hands, and lots of patience are needed. At first you may feel like you are making no progress. Just keep doing it, gently, gently, gently.
I do not think the Chambon would have worked so well if I had not done the 5 months of work on reaching for contact, accepting contact, accepting my leg signals (I had to wear spurs, such fun with a tense mare but she balked.) Those 5 months I satisfied her that being ridden was not a torture session, after the Chambon she started moving freer even in the pasture and came to enjoy being ridden.
YMMV