Going back to the brilliant diagram of 'Runaway Gun', the first Blue track could be a curve due to increasing precession of the DI gyro. So where do you reset the DI to Compass? and will this not upset the correction heading angles required? as you will also need to add or subtract this DI/Compass error.
Theory is Ok in some academic cases, but has its limitations in practice. (The cross-wind can alter from Start to Finish.)