Tongue Issue in Young Horse

My 4-year old gelding has started sticking his tongue out under saddle recently and I’m looking for additional suggestions for preventing it.

When he does it, it’s always the right side of the mouth. Lifting the bit/rein straight up will get him to pull it back in but we go through 4-10 repetitions of tongue out, lift the rein, tongue in, back out, lift the rein…The trick is catching it quick enough without constantly leaning over to watch his mouth.

I had a bit fitting and he has “sharp bars” but no other significant findings except somewhat hard ridges on his palette. Vet check was unexciting but had a cap on each side that had just come off, and she could feel small bumps where his canines will erupt (which may take a while yet). Neck, poll, and back all felt good and “springy” to the vet. Saddle fit was checked and adjusted as well.

I’ve tried a Happy Mouth mullen, Bombers ultra comfy lock up snaffle (bit fitter’s recommendation), and HS KK double jointed snaffle. I’ve done a loose crank noseband, a little bit tighter crank, added a flash, and pulled the whole noseband completely and nothing has really changed, except the flash possibly helped a tiny bit.

He mostly starts it at the walk on “contact” (which is very light and very unsteady currently) but will do it some at the trot and I’ve just started seeing it for a few strides at the canter. He doesn’t start the ride doing it - it’s either when he’s maybe a little bored or tired, but he’s only ridden for 20-30 minutes and usually still has energy left. He doesn’t do throughout the whole ride but I can’t avoid the “triggers” completely (walking with slightly shorter rein) and it’s becoming more diffuse with less of an obvious trigger. If he’s super distracted or focused on something like a trot pole, his tongue is in.

It’s always the right side, and he seems to like holding it or maybe sucking on it a bit. He’s a very, very, very oral horse who is always chewing on something unless I’m right there - cross ties, his tie rope, etc.)

Training and/or equipment wise, any suggestions to resolve this immediately? I feel like he’s a horse that likes habits and don’t want him to develop and reinforce this as a habit.