I'm prepared to believe that they were one song with two tunes, but we did sing them as 2 separate ones: guess the 2 tunes tunes would also harmonise with each other.
Have listened to the Michael Mitchell midi and that corresponds to what I knew as "My paddle" etc.
For "Land of the Silver Birch" we sang (if in Amin)
Land of the Silver Birch
A      AA      EEE,
Home of the Beaver
A      AA    E E,
Where once the mighty moose
A'       GA'       GEC
Wandered at will
DD       D E,
Blue lake and rocky shore
A'       GA'    GEC
I will return once more
DD    D ECA,
Boom diddy I dee Boom diddy I dee boom diddy I dee boom
A      AA   AC    A    AA    AC    A    AA    AC    A