Contrary to my belief no one's listed the Apes trilogy yet. I thought for sure 1SO would. Didn't he say something about it being the best current action franchise last year?
I didn't even consider the Apes trilogy and I think that's because I'm still feeling burned by the severe change of tone away from action adventure in the 3rd film. Much like back when Mad Max was a proper trilogy there were two great films followed by Thunderdome, which had the look and feel of Mad Max, but the story went to a place I never wanted Max to go, giving hope and saving children. It tainted the entire trilogy for me even though I wouldn't say Thunderdome is a bad film. It's just too radically different.
Series that do not meet my definition of trilogy: Alien, Mad Max, MCU movies, MI, Rocky, Terminator, James Bond, other things
I asked a friend at work for his favorite and his answer tickled me. "The Fast & Furious trilogy that contains both Paul Walker and The Rock."
Your exclusions are interesting because by your very reasons for excluding them...
Star Wars is a series of what will be 9 films. So calling your favorite the "Original" trilogy is the same as saying Rocky I - III or the first 3 Alien films.
Lord of the Rings stopped being a trilogy once Peter Jackson unleashed The Hobbit. It is now part of a series.
The Dark Knight trilogy are just 3 Batman movies from a large and ongoing franchise. By your own definition, not a trilogy.
The Apes... well you can see where I'm going. The 3 latest films even make sure to connect to the previous Blockbuster franchise. I can see excluding the Tim Burton film, but the other 8 films bust the definition of trilogy.