IIRC the "Only Playing Leapfrog[s]" variant hasn't figured here yet. It resurfaced in Theatre Workshop's composite theatrical presentation Oh What A Lovely War, directed by the first Mrs Ewan MacColl, Joan Littlewood,

---"stage musical Oh, What a Lovely War! that Joan Littlewood and her Theatre Workshop created in 1963, which was itself inspired by "The Donkeys," Alan Clark's 1961 attack on Gt War generalship", Wikipedia---

in the form "One staff officer jumped right over another staff officer's back[x4 ~~ They were only playing leapfrogs[x3], When one staff officer jumped right over another staff officer's back."

~M~