Jim,
The staff officer song didn't go on ad infinitum in my hearing. I think it's elswhere on the forum but I have always heard the verse as you described but the chorus was

They were only playing leapfrog (x3)
when the first staff officer jumped over the other staff officers' backs.

But to address part of the original question,

She wears her silk pyjamas in the summer when it's hot,
she wears her flannel nightie in the winter when it's not.
And sometimes in the springtime and sometimes in the fall
she jumps between the lilywhite sheets with nothing on at all.

Often followed by
Oh, Sir Roger do not touch me (x3)
As she jumps between the lilywhite sheets with nothing on at all.

and the chorus losing one word of the first line at subsequent repetitions.

Cheers, Rowan