"My Anna played piano on a hunk of two by four"

ór

"My Anna played piano with a length of two by four"

was, I am 'almost' sure, simply one of the lead lines to

"A sailor man from Turkistan came knockin' at the door"....Walt seldom had Churchy or Howland or Pogo or Albert DO a complete song..(remember, most of these were in 3 panel daily strips).....and "Anna played pianna" was tossed in at a different time than "Mamie minded Mama"...maybe a year or two apart. ("Deck Us All" was done in various degrees of completeness on various occasions.)

Part of the point of what Walt did was; that people mess up, forget, change, invent and mis-hear stuff...the characters were forever amusing us by being us....