The only way to do it successfully was what Roger did: an entirely different style and tone for Bond.
Well you know what they say about hindsight being 20/20. Director Guy Hamilton instructed scriptwriter Tom Mankiewicz to remove Sean Connery's signature lines from the Live and Let Die script and Guy Hamilton made certain that Roger Moore never said or did anything that would allow him to be compared to Sean Connery or the character The Saint. Recall how Roger Moore does not drink vodka martinis, smoke cigars instead of cigarettes, and never says "The name's Bond, James Bond" in Live and Let Die and The Man with the Golden Gun. I think that this gave Roger Moore breathing room and it allowed him to assume the mantle of the James Bond character.
I also think that film goers and the press had to get used to the concept that Sean Connery did not want to play James Bond ever again. So fans and the press had to put up with Roger Moore or give up on the idea of seeing new James Bond films.