You are correct in that many, but not all, cajun speakers use the "mon" sound for what is "moi". Some even say "mo". There are a lot of these pronounciation differences that might throw someone used to hearing standard french.
The last line does not make sense because the transcription in the liner notes is wrong.
He simply sings : « Hé, c’est par rapport à ça t’as fait mais avec moi »
(......................I would never marry
Hey, it’s because of what you have done with me).