I wonder if that method for determining the South is accurate enough. 20 ft is not very far, so a few inches off and your South is wrong enough to cause serious alignment problems. Is there any way to can see things about 200-300 ft away and determine a point that is exactly south of where the dish is? Either by looking on google map, or maybe with your GPS method?I use the longitude readout from GPS to determine true south. I walk about 20 feet in front of the dish a set a stake where the longitude is the same as the dish location - that should be my true south reference. I tried the compass in a phone but found that wasn't very accurate so I don't use any of those apps. I did a string test just a few days ago and that turned out OK. I'm not sure about feed centering though. There doesn't seem to be an easy and accurate and inexpensive way to set it. I'm trying to fabricate a laser pointing solution - see the images of my first attempt. I don't think a tape measure is a very accurate way to center the feed but I'll probably give that a try.
However, I also think that the alignment might not be the main problem here, and that the core of the problem is with the dish/feed/LNBF. That's the one to tackle first.
Did you check the focal length? Does it match what the brochure says? If I remember well, there was a Tek2000 dish that had some problems in that department, so I guess it's worth double-checking it