If you want to cut up your polygon into squares, one thing you could try is:
- get minimum bounding geometry (envelope, something with a rectangular/square result)
- create grid from minimum bounding geometry (check out Ian Broad's custom grid tool http://ianbroad.com/creating-quarter-quarter-section-grid-python/)
- convert your polygon to line
- merge polygon line with custom grid
- convert merged lines to polygons
- select split polygons by locations having their centroid in input polygon
The result will be a polygon cut into squares/rectangles, except for the irregular parts that you can identify by getting the ratio of split polygon calculated area divided by the calculated area of the split polygon's minimum bounding geometry.
EDIT:
This methodology could still work for what you're trying to do; for the minimum bounding geometry, use rectangle by area, and using Ian Broad's tool just put in a value for the horizontal divisions and 0 for vertical divisions.
Edit:
Here's my split polygon using this methodology. The green line is the minimum bounding geometry using rectangle by area.
