Just as a point of clarification - there's nothing written in stone that says just because you are LDS you have to have a "LDS Funeral". If you choose to have the funeral at an LDS chapel, it's subject to Priesthood direction and will need to conform to the CHI. However, if one wants to deviate from that, there's a whole world of possibilities out there.
From my personal experience - my Dad died about 8 years ago. He hadn't been active in the Church since he was 12. In all likelihood, I could have had his funeral at an LDS chapel, but chose not to...no one there would have known him and really he didn't want anything held anyway. We had a short service in Las Vegas (where he was living) for family and some of his old pilot friends. We then flew his body to Ogden, UT for burial where we had a brief graveside service just for family and I dedicated the grave. That was it.