What I think now after more consideration is that the error of 1 degree 8' does not necessarily translate into 68nm between assumed and actual position.
To my understanding, an intercept (difference in computed and observed altitude) is exactly the difference along
the azimuth from the assumed position to the celestial line of position.
Actually, it occurs to me you could be plotting the intercept in the wrong direction.
You should be plotting the azimuth line towards the the sun and through the assumed position. Sounds like you are indeed doing this.
If the observed altitude is greater than the computed altitude, then you mark the intercept in the direction of the azimuth. If the computed altitude is greater, mark the intercept in the reciprocal direction. For example, if the azimuth is SW and computed altitude is 20 degrees, then:
- observed altitude 18°52' --> intercept is plotted 68 miles SW of AP.
- observed altitude 21°08' --> intercept is plotted 68 miles NE of AP.
If you plot it in the right direction, you should be just right.
If you plot it in the wrong direction, then you will be approximately 136 miles wrong.
In general if your error is double one of the numbers involved in the computation, sounds like a positive/negative or direction problem.