NavList:

The best case for a sun-compass landfall without taking additional observation is if the azimuth of the sun is not changing. This happened on July 2, 1937 when Aamelia Earhart was attempting to find Howland island. The sun rose on that mornig on an azimuth of 067 true and remained on that azimuth for more than an hour. This caused the resulting LOP to run 157-337 for that entire period. So, after they intercepted the LOP and turned to 157 and maintained that heading either with a compass, directional gyro or with a sun compass they were not able to find the island without additonal sun shots which were prevented by clouds. In flidght navigation the error in dead reconed positions is 10% of the air distance covered. so if they intercepted the LOP 100 nm out then a possible error of 10 nm would reasonable on the run in.Add to this the possible error of 7nm in the observation itself means that their flight path could be 17 nm off to the side of the LOP, thus missing seeing the island. 

Now looking at your idea. Let's say  a similar attempt was being made in the normal situation in which the azimuth is changing creating a LOP that basically rotates on a pivot pin at the destination. So, again, Earhart intercepts the LOP on an azimuth of 157 to the island, and changes heading to 157 and fixes it with a sun compass. This means that she is starting off northwest of the island. But now the sun moves across the sky until its azimuth is 360 at noon and earhart had always kept the sun on her left wihgtip. As she does this she gradually turns to a heading of straight east but. since she was to the north of the island at the start, this means that she remains to the north and passes well to the north of the island while on a heading of 090. As the sun continues to move to the east then Earhart will eventually be heading off to the northeast, never comming close to the destination. 

That's why your idea doesn't work.

gl