Mariette,

since you seemed to have tried everything, and he is still rubbing his face, he may have facial neuralgia associated with former bit use.
The pressure from the bitless bridle can trigger the rubbing response.
Even though the bit is removed, the nerves in his face are still super sensitive.  I spoke with Dr. Cook about this before responding.
Did your horse do this in his bitted bridle?

You can try having very little pressure on your reins, or padding the bridle up with a thin piece of fleece.

If your horse is very responsive try riding in a halter with two lead ropes just as an experiment to see if the looseness of the halter fails to trigger the rubbing of his muzzle.

I have spoke with people that have used the bitless and their horses still seem in pain from the noseband, because it can sit directly on the area where the horse has a bone spur that was created by former bit use.

I know personally that in many cases that I have revisited horses that had exhibited painful facial expressions, continued to raise their head when asked to halt or back up, still rooted jerked the reins out of riders hands etc. etc. gradually became better with each painless ride.

Because they had experienced years of pain as soon as the bit was placed in their mouth they just assumed being ridden would be painful.

Hopefully your horse will become better with each ride.

I am told that the rubbing may or may not go away depending on each individual situation.

Good luck keep us posted!