NavList:

Thank  you Frank for the very patient guidance on moderating Azimuth delta with cos (Alt).
My numbers are now within 8 seconds (of time) of Lars. And within 4 seconds (of time) for Frank's Stellarium technique.

Using Moon Alt to squish Azimuth delta

2023-Oct-14 17:07:48 Sun LL is covered by the Moon
2023-Oct-14 18:20:40 Sun LL is covered by the Moon

Using SunLL Alt to squish Azimuth delta

2023-Oct-14 17:07:49 Sun LL is covered by the Moon
2023-Oct-14 18:20:40 Sun LL is covered by the Moon

My "test" is now:

delta_az = (sunLL_az - moon_az) * cos(moon_alt * PI / 180.0); // Frank Reed's advice about squishy Az degrees
distance = sqrt( pow( (delta_az), 2 ) + pow( (sun_alt - moon_alt), 2 ) );
fprintf (fresults,"%s ",sundate);
if(distance <= radius_of_moon) fprintf(fresults,"Sun LL is covered by the Moon\n");

Ephemeris data from:
https://ssd.jpl.nasa.gov/horizons/app.html#/

Assumed position = 28.00° N, 90.00° W,  0.0 metres Elevation.

Date__(UT)__HR:MN:SC, , ,Azi_(r-app), Elev_(r-app),  Ang-diam (arc seconds),

2023-Oct-14 18:20:40,*,m, 194.280045,    52.806141,  1924.160, SUN
2023-Oct-14 18:20:40,*,m, 193.862550,    52.538572,  1828.926, MOON

Thanks to Frank, Lars and Kermit.

Regards, Geoff Hitchcox, Christchurch, New Zealand