The answer depends on what you prioritize in this situation.
Hold tight, continue training as normal
As you've noted, suggestions and positivity aren't helping. You've mentioned it is unpleasant to train there - which tells me it's not just rough times when it involves the head teacher - there's problems in the local group's experience as well.
There'll be less people to train with, presumably less fees coming in, and financial hardship and probably eventually closure.
Benefits: You maintain whatever relationships you have with the local teachers/students. You get to continue whatever quality of training you're currently getting for a period, before it becomes completely unteneable.
Drawback: Nothing really gets better and it eventually gets worse.
Try to form a separate, recognized training group
If recognition and sticking to the core lineage is important, you might organize a group who decides to deal with the head teacher's requirements and form a seperate group/school. This will be seen as a power play, burn tons of bridges with your local teachers and some of the other students as well.
The head teacher may not accept it either. Or, the head teacher uses your group as a "weapon" to basically prop up and make the your current teachers look bad.
The only time I've seen this be a reasonable option is if the local teachers are corrupt or messed up in some way - for example, one of the schools I trained at it became clear the local teacher was stealing from the students (like, their actual belongings) and spreading rumors between the sub teachers in some kind of weird mind game.
Benefits: You get to stay in the official recognition of the lineage. All the suggestions to try to work with the head teacher? You can enact them. Drawbacks: It's a lot of work. The head teacher may turn out to be entirely worse than what you know of so far. You burn a lot of bridges and lose friendships.
Form an informal, unrecognized training group
You need to train and you need people to train with. You may not have all the space and equipment you want, but you can still train with other folks who love the art and also don't want to deal with the politics. Your operating costs are low, which means you're not dependent on pulling in more students to keep the lights on.
However, it also is hard to pull in new people as well, since most new people are brought in by being impressed by a nice school, uniforms, and official recognition.
Benefits: Training! Not having to fight with people over politics. Drawbacks: A few folks will see this as "abandonment". You won't have official recognition. You won't benefit from the shared resources of the school - the space, the equipment, etc.
You can pick training, maintaining relationships, or staying official, but you can't get all three, unfortunately.