I read a couple of replies before posting this, and it seems I might have a different outlook.

I think there's a lot of great advice on here, but it ignores what you need to prepare for, which is the worst possible outcome. For most people, sex is a non-negotiable part of a relationship, and I'm guessing you would not be able to be married to someone you're only having sex with once a month.

By all means try, take her feelings into consideration, but be aware that this may mean that your relationship will eventually deteriorate. The same way you shouldn't be mad at her for not wanting to have sex, she shouldn't be mad at you for wanting it.

I hope it all works out, as I think a lot of guys would just go and cheat. You're trying, and you clearly lover her as a person. Good on you.