It sounds like a LOA is your only rational option.
Unless you had significant knowledge gaps, two months of prep was excessive to begin with. All the data indicates that 4-6 weeks is optimal, with 5 weeks usually being the sweet spot. Beyond that and exhaustion and burnout set in (as you are well aware).
So take the LOA, take a break, and then hit it hard with a 5-week study plan. Do not schedule your exam right up against January rotations, and do not push your date back again unless you lose a limb. I've seen many students get stuck in the cycle of study, burnout, procrastinate, push the test back, study, burnout, procrastinate, push the test back, and so on.