As for "Paint Your Wagon" and "They Call the Wind Mar(eye)a, both were from the pen of Alan Jay Lerner, an east coaster who may simply have found it sounded right in the song. I would have thought he might have opted to spell it Mariah.

In my neck of the woods, hard by the Mexican border, Mar(ee)a is the only pronunciation known locally.

Now; how many songs can you name with Mar(ee)in them?