Odd Columns Out

I see your 159, and raise you 3 and 7. My hand is strong, so I’m willing to keep raising if I have to.

This one also had some testing contoversy, with difficulty estimates and solve times ranging widely.

Rules:
Normal Sudoku rules apply.
Digits in columns 1, 3, 5, 7, and 9 indicate the column in which the digits 1, 3, 5, 7, and 9 respectively appear in that row. (For example: If R2C5 were 7, R2C7 would be 5, but if R2C5 were 2, R2C2 would be 5.)
In cells separated by a white dot, digits are consecutive. Not all dots are given.

Estimated difficulty: 1.5 out of 5