I had an odd problem that originally brought me to these boards thats similar to this. All of my DVRs in the house wouldnt get odd transponders. Then every so often everything was fine, then every so often half strength, but more often than not I had no odd transponders.
At any given time, I could hook up my 1 DSX5500 to any feed in the house and it would work fine.
After replacing my pretty Phillips DVR with an ugly Samsung I had a service call scheduled. They replaced one connector for no reason (to no avail) just to test (they were in awe of my wierd problem) and then replaced the LNB/Multiswitch portion of my Phase 3 dish just as a troubleshooting step and that fixed the problem.
I'm not saying this will fix your problem, and it may not even be an option really... but they're not very different symptoms if I'm reading everything correctly.
I'd call DirecTV, you'll end up at the second tier of tech support because front line guys cant replace HD IRDs and you've done everything in the Searching for Satellite script. Clearly explain everything you've done and see what they say.