Last week I listened to the first disc of the deluxe edition of More of the Monkees, and a couple days ago, "Ladies Aid Society" was in my head when I woke up. According to Sandoval's The Monkees: The Day-by-Day Story of the 60s TV Pop Sensation, the track itself was recorded in late August/early September 1966 (around the same time other tracks on More of the Monkees were recorded) but wasn't released until The Monkees Present in 1969. I don't have The Monkees Present, but from what I understand, the bonus track on More of the Monkees is the same recording. It's just a mono mix where The Monkees Present uses a stereo mix.
Because the song was stuck in my head, I realized that it has sections in different time signatures. The verses - sung by Davy Jones - are in 4/4, but the choruses - apparently sung in falsetto by some of the session musicians - are in 3/4.
The only other song I can readily think of that also has sections in 3/4 and 4/4 is the Beatles' "Lucy in the Sky with Diamonds." According to Mark Lewisohn's The Complete Beatles Recording Sessions, "Lucy in the Sky with Diamonds" was recorded in early March 1967. So the half-3/4, half-4/4 time signature of "Ladies Aid Society" predates that of "Lucy in the Sky with Diamonds." It just wasn't released until years later.