I'm just like you, I haattedddd asking for LORs. Email is definitely the best way. I notified them 5 months before the due date, but I told them the due date was a little earlier just incase someone ran behind (and thankfully I did it, because one professor did). For example, I told them all the apps were due December 1, even though some were due the 1st, some the 15th, and some January 1st.
The emails was basically as follows (please note these are example sentences & not exact replicas)
Dear XXXXXX:
Hope all is well! (filler sentence about a class we have together/ project we're working on/ thesis update) As you know, I'm applying to a few Ph.D programs this fall. I am wondering if you would be able to write a letter of recommendation on my behalf (this isn't exact wording but it's very close). I am applying to programs in XXXX with a concentration in XXXX. (then I talked about my study plans, the schools I'm applying to, the research I plan on conducting, etc.)
(here I wrote why I would love for them to be my recommender -- why I think they know me well, maybe a great class we had together, etc. Here I told one professor that I had mentioned her course in my SOP, which is why I would love a letter from her ). The applications are due December 1. I completely understand if you are unable to write the letter for any reason. If you are able to do it, let me know if I can provide you with any information that would be of assistance, blah blah blah
Talk to you soon!
Regards, XXXX