Steve Carlton played for 24 seasons, it's true. But only 14.5 with Philadelphia. Kaline, as you noticed, is also incorrect. Close, but not quite enough seasons.
Incidentally, the correct player was one of the first people (after Banks and Musial) that I thought of as correct answers to the Al Kaline question, despite an underwhelming lifetime BA of .267, and only 268 career HR's. Also, I'm not sure if he had a team-related nickname, but my point is that he had a couple of seasons batting above .300, he was something of a slugger, and he's not someone really obscure.