We had a similar problem with two of our locals (both owned by the same company) here on Hawaii last year. Similar to your issue (bear with me here), the station broadcast quality on DISH was SO BAD that the channels were unwatchable at times. This problem took close to 4 months to resolve.
In some instances, you would watch a program like a hockey game with fast moving action and the picture was so choppy that the action seemed to jump from frame to frame.
In other instances, the pixelation problems got to a point where the picture would freeze for up to 8-10 seconds in a pixelated state. When the picture returned, we would be thrust ahead into the program so that we would miss the chink of time for which the picture was frozen. This could occur every few minutes or several times a minute.
First - post your problems on the DirectTV forums. It turned out that a guy who had DirectTV was experiencing the very same problems that we had on DISH. This gave a more direct idea of where the problem could emanating. See if the other satellite service is having the same issue. Not everyone reads this website and not everyone speaks out when they have these issues.
Second - As already mentioned - call the engineering department at the local station and speak with the chief engineer. I spoke with the engineer and found that cable TV had a direct feed from the control room. I was told DISH and DirectTV signals were picked up on an OTA antenna and fed to an upload location in Colorado. As a result of this info, I passed it along to DIRT and the DirectTV guy passed it along to DirectTV support. We were able to show that both services were experiencing this problem.
Third - if you can capture some of the worst problems you are experiencing - post the video here. Be specific with how often you experience the problem. Be specific that you tried the SD feed and the HD feed and that the problem occurs on one or both feeds. Also mention to DIRT the experiences you and your friend have had and that they are the same (eliminate your equipment and installation). Also speak with DISH support and make sure they filed trouble tickets. Get the numbers of the trouble tickets and keep cross referencing every time you call or send email.
You already said you ran into the issue where when you call in, they say, "nobody else has complained" and they discount your credibility. This is a constant battle. Post often to this thread as well as what you do with DIRT and DISH support. As I said before, this took close to 4 months to fix for us in Hawaii.
The key is - be as specific as you can with all troubleshooting steps and observations. Experience showed that DISH is not going to do the footwork for you. It's a shame but keep at it.
Do a search for KGMB / KHNL problems in Hawaii on this website and follow the thread that we kept up to get our resolution.
Good luck - and you can always threaten to contact your Better Business Bureau and State Attorney General to complain about breach of contract. DISH had advertisements awhile back saying that DirectTV had lots of Better Business Bureau complaints and DISH did not.