Out of curiosity, I revisited the original method and updated it to be in-line with the polar method (same assumed forced radial displacement, point loading at start of contact not in middle of angular increment, etc). The result gives a bending stress of 196.7 MPa. Although it hasn't been checked, and as rothers has highlighted, the stress is close to FEA. Attached is the revisited file. Looks like this particular analytical method has been finalized!