Just a question, and I hope I can be forgiven for barging in...
I very much hope to become a British citizen. My reasons for this have nothing to do with my feelings about America. I love America, and I will always be an American. There is no question (hoping for dual citizenship, but unsure of legal grounds there).
Anyway, my reasons for this are many. The main one is my feelings about immigrants in America. I live in South Florida. I think immigration is great, it's wonderful to be able to offer people from different nationalities a new hope or an escape from terror.
BUT...
There are some here who are not grateful at this chance. They get very upset when asked to show the slightest loyalty to America (where some have been longer than you have been in the UK). We hear statements here like, "You have to understand, we don't WANT to be here...we want to go home." They refuse to become citizens. They refuse to contribute to charities that do not have to do with their "home". Their anti-American statements can be quite offensive.
As I said, I think it's great for people to come here. I welcome them. But I think it's shameful to take advantage of another countries' welcome and refuse to give anything back.
I am not in any way implying that this is what you are doing by not becoming a UK citizen. Please don't think I am. Just try looking at it from the UK's angle, maybe that might help you with your decision.
I personally don't think that swearing loyalty to the UK or HM is necessarily renouncing your loyalty to the US. As I said, I hope very much to become a UK citizen...I feel kind of like I owe that to a country willing to take me in. But I plan to still celebrate Thanksgiving and the 4th of July (although the latter perhaps quietly.) I understand your feelings about the oath, and also about not wanting to take sides. But for now, the two countries are allies, and hopefully always will be. Swearing to support the country where your home is doesn't mean refusing to support the one where your heart is. (At least I don't think so.)
If it ever comes down to battle, you have a tough decision to make...but the decision to fully be a member of a society and country in which you have lived for 35 years doesn't seem disloyal to me.
I hope maybe I've helped....it is of course up to you, and I hope you don't think me critical.