Moved the dish in alt and az about 0.25" max before things fell apart. They never got any better. I did no better with rotating the LNBF. Looks like I'm close to the sweet spot, but just can't get to it.
Here are my manual scans (in % quality):
11705 H 55
11788 H 70
11789 V 70
11835 H 60
11836 V 60
11866 H 33
11867 V 33
11897 H 45
11898 V 37
11928 H 33
11929 V 33
11990 H 37
11991 V 37
12021 H 37
12021 V 37
The rest are just at 36% signal strength (noise level):
11779 H, 11874 H, 11879 H, 11936 H, 11999 H, 12010 V, 12052 H, 12053 V, 12060 H, 12083 H, 12084 H, 12090 H, 12115 V, 12122 H, 12145 H, 12146 H, 12152 H, 12177 V.
Curiously, I couldn't even find 11966 or 11965. I think it's time to call in a professional installer. Perhaps he can get me there or offer a good deal trading up dish size?