A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robin Jouan
Date: 2017 Jun 7, 02:13 -0700
Referring to your excerpt of FAA handbook, the example of figure 12-15 can be directly solved via the method of Coplanar Vertices.
No need to use the North pole or any arbitary point as an intermediate. No need to draw any LOP on a map template.
Starting from FAA data, the result I find is :
88° 42.1' N 17° 25.5'W
Nevertheless, the approach of the FAA handbook is interesting and illustrative of LOP method in an extreme case.