I think that you are right to consider you may have to move on from both of them. If you cannot choose, and they are not happy with a poly relationship, then it will be miserable for everyone involved to stay.
I know you can love two people. I never thought so before... but like you said, I get very different needs met from my partners.
I wish you luck... I don't have much advice. I do think you're right to be concerned about your fiance wanting to do it to make you happy when it's not something he's really comfortable with.
I'd do some online research and show it to your fiance and your best friend. That might be the easiest way for them to understand.