Wow, this is a huge thread! (New guy here.)
This is absolutely a part of me as well, and it runs in my family. My mom's mom loved spoonerisms (e.g., "You have deliberately tasted two worms! You may leave Oxford by the town drain" instead of "wasted two terms" and "down train"). My dad was constantly making puns. He also once authored a 5000-word sentence that was grammatically correct.
As a teenager, Marshal McLuhan introduced me to pithy quotes from James Joyce's Finnegan's Wake, which is linguistic invention from beginning to end. I spent several years around that time experimenting with what the Victorians called "automatic writing" in a similar spirit, mixing bits of different languages together and playing with word roots. I especially liked to pile predicate on predicate, with the explicit goal of making the reader forget what was the original grammatical subject, and then realize that the identity of the subject did not really matter any more. Parentheses within parentheses, and who cares about the original things! We are adrift in the sea of parentheses. Meaning exists only in relation to other meaning and the unconscious is structured like a language, as that other famous word-player, the French psychoanalyst Jacques Lacan, said. I also used to love the philosopher Jacques Derrida's word play.