NavList:

Dear Sir,

Although I have not worked with the US Heights and Azimuths Tables in eons, I will attempt understanding the reason of your own surprise.

As per your own computations, the Sun GHA at 11:03:22 is equal to 344°36.8'.

In other words, the Sun Meridian on Earth is at E015°23.2'.

A fitting longitude to get an integer LHA would be at E015°23.2' and this integer LHA would be simply 0°, which is to give you a 180° Azimuth.

On a complementary and related topic, you should already expect an actual Sun Azimuth very close to 180° since your Chart / DR Meridian is at E015°44.0' while the Sun Meridian is at E015°23.2' with the Sun subsolar point on Earth being at over 1,800 NM from your DR position.

From the Sun declination at N22°32.9' and your True Altitude at 59°29'0 (which I understand it as directly comparable to the Tabular Altitudes, i.e. as being a geocentric altitude) your Observed Latitude is to be very close from :

{ N22°32.9' + (90° - 59°29.0') } , i.e. very close to N53°03.9' , which is almost 180 NM away - and due South - from your charted position ...

... a bit unusual and strange.

Then I am probably missing your own point, yes ?

Kermit