Hello,

This seems complicated.  Are you commenting what to do about the teachers removing grade points due to handwriting?  If the answer to the question is correct, then it is correct.  A paper is to determine if a student understands the subject of study, not handwriting skills unless of course it is a writing assignment.  You mention that you can read what he writes so seems to me that any reasonable person should be able to read the answer too.

If he is having difficulty with handwriting, you should meet with the teacher and discuss having his fine motor skills evaluated and a therapist through the school can begin working with him to help him develop better writing skills.  I'm surprised that the teacher has failed to suggest this already, but you did mention that it is a private school and these services may not be available.

If the later be the case, you can speak with his pediatrician and they can recommend or arrange an appointment for an evaluation.

Basically, I understand that he has asthma, but has not actually been diagnosed with ADD and that is only a suggestive comment, you mention that he has good grades and basically performs effectively other than boredom.  Becoming bored has little to do with ADD, sounds like the subject or teaching practices are not inventive or challenging enough.  

Teachers are usually attentive to the parents concerns, and where you are paying for the instruction from a private school, I would imagine they would really be accommodating to your needs.  Talk to the school concerning these matters and seek a resolution, you may want to practice writing with your child at home or seek a tutor and/or therapist to address motor skills.

I would try to arrange with the teacher not to score his papers based on handwriting ability but on content and let them know that you are helping him every way you can to improve his writing skills and would appreciate their suggestions and support.  If they are critical about his writing he is less likely to feel motivated to improve, a little encouragement can go a long way.  

You didn't mention if his writing was in print or cursive, but education.com does provide good worksheets to help practice.  Since the school does not have an award incentive in place, you may want to tempt him with one as he improves or practices, maybe a new game, night out, or whatever would inspire him.

Best wishes!

I believe a new school will only make matters worse for him. Attention Deficit Disorder causes an inability to focus. Taking him off the meds will also make it worse for him because the medication deals with both focus and conduct. Put aside 2 hrs every day working puzzles, setting and going over his home schedule and allow him to verbalize and organize his thoughts about how his day at school went. Thinking makes his reactions slower and you will find that his handwriting will improve.

This helped my son with ADHD.

You kinda got a lot going on in your question. From my understanding, however, just because it is private school, it does not mean your child cannot have services rendered to him if he needs it. You might want to look it up on your state website or under your school district website. You don't want to move him because teachers are doing their job. It is a private school, and with that usually comes a higher expectation of the students.
And just make sure you do not use his add/asthma as a crutch and a reason he does not do things properly.