This is an important topic and I feel strongly about adding my opinion to it. I would like to begin by saying that I often come off as being harsh or short when I communicate, so I hope that I don't offend anyone.
Based on some of the statements that you have made, it seems to me that you have a somewhat distorted view of how religious people view and worship their higher power. Being an American, I believe totally that a person has a right to believe as his or her conscience dictates. I am a leader in Cub Scouting not just because I was called as one through my church, but because I share BSA's view that a person's spiritual growth is just as important to their well-being and improvement as a citizen as are physical and mental development. I get the idea that as BSA's spiritual aspect becomes more evident as your son progresses, you are becoming increasingly resentful of it. In answer to one of your questions, quite frankly, if you recite the Cub Scout Promise, you are being hypocritical, at least in my opinion. That to me is like going to another country and pledging allegiance to their flag or nation, and still calling yourself an American. (By the way, the "under God" part of our pledge was added for political purposes, and I don't think it should be there, but I digress.)
I think that you should seriously consider having your son get involved in an organization in which faith is not a factor. I would also suggest that you open your mind to the fact that the vast majority of people on the planet believe in some religion, and maybe there is something to it. I investigated different philosophies (Christianity, Judaism, Islam, Buddhism, Taoism, etc.) as I grew up, until I found the one that truly spoke to my soul.
At any rate, as you told your son, the BSA was founded by religious people on religious principles, and it's a private organization that asks you to follow its rules if you want to be a member of it.