What do I do if this "doctor" (she's actually a nurse practitioner) will only prescribe for 200 mg/day?
My suggestion would be to let the ILADS Treatment Guidelines
do the talking. That way, your doctor is reading the recommendations and evidence of other doctors who treat tick-borne diseases, versus listening to a patient.
Without supportive material and justification, your doctor may not be willing to go outside the "standard of care." After all, they are beholden to medical boards and don't want to lose their licenses. So, help them help you.ILADS Treatment Guidelines
1. Go to https://www.ilads.org/patient-care/ilads-treatment-guidelines
2. Scroll down and click "Download ILADS’ 2014 Evidence-Based Treatment Guidelines"
3. Use the Search tool to find "Q1." (Question #1) You should find two instances.
4. The first "Q1" and corresponding answer is brief. The second is a detailed discussion.