Hi Folks.
      The version I heard originally was only a tiny bit like yours.
It was an Australian Army poem with a sung chorus which went.

"Oh Roger Rum. Oh Roger Rum. Sligga marig menorium. Oh Roger Rum!"

Sung with beery gusto which got worse as the evening wore on.
The only verse I can remember is the first one.

"So when Roger Rum was just a lad, He did earn a precarious fee.
Leading blind whores from the brothel doors,
down to the river ,,,,, to pee."

Cheers. Regards Bob.