I was in the same boat last year--couldn't take my neuro rotation until August. I just asked my neuro attendings towards the end of the month if they would write a letter for me. The letters were submitted and then downloaded by the neuro programs by the end of Sept or beginning of Oct. You just have to enter the names of the doctors writing you letters on our ERAS application. The doctors actually send the letter to your school (I think) to be uploaded to your application. Then the residency programs download the letters at their leisure. So, you should be able to enter the names by early Sept and submit your application. It will be okay if the neuro letters aren't uploaded for a month or so. I still received interviews before my neuro letters were received.
Also, I would suggest trying to work with at least two attendings during your neuro rotation. I think it is good to have more than one letter from a neurologist (but that's just my opinion).
I hope this helps!
