How long has the fatigue been plaguing you? I had fatigue that affected me in a similar way for about 5 months last year, with a similarly demanding job. It turned out to be due to a relapse that had few other symptoms, and I feel loads better now and back in good form work-wise - so if it is a recent problem please consider that possibility!
But if you’ve ruled that out and it’s definitely permanent - please give serious thought to the part time option. You say you don’t particularly want to cut your hours down but you may need to think seriously about your reasons and priorities.
Personally, I work 80% hours as I have just kept to the hours I had when my daughter was small. My original long term plan was to return full time when she got to about the age she is now but I have decided against that since being diagnosed with MS. I could afford to stay part time and that was the best option for me, a really positive choice. If you can afford to reduce your hours then it’s a good option and has been a good experience for me. If you are good enough at your job (sounds like you are!) then you will still be valued by your employer and colleagues after going part time.
Hope you find a solution x