GJK, for the Carousel setlists I'd say that BklynBlue would be your best bet, as he's most likely listened to and studied these tracks more than anyone. BTW, the dates for the recorded show(s) there are open to question - they may well have been from later in the month. Another reason to order "A Love That Burns" - the excellent e-book that BklynBlue (Rich Orlando) recently published.
As to the Kinetic Playground shows, the band was certainly busy in Chicago, but we know they did indeed play those shows on Jan. 3 & 4, 1969, since there was a review of one of those shows in the
Chicago Tribune - partially quoted in Christopher Hjort's "Strange Brew" book - another invaluable resource.