A few observations:

1. If the problem is getting the airline to respond, have you considered trying to get a travel ombudsman involved? There are a number of them out there (Conde Nast Traveler magazine comes to mind, also one that is quoted on WebFlyer). Since they have the ability to publicize lack of cooperation in a nation-wide or world-wide forum, they can often command attention.

2. I was also a member of Qualiflyer before they went Tango Uniform, and would have liked to transfer my miles into LH, but as I recall one didn't have a lot of choice. If I remember correctly (and you might want to do a search in the Qualiflyer archives), you had to have earned the plurality of your Qualiflyer miles on LOT in order to transfer them to LH.

3. And, I think someone (Marvella?) commented on how slow Qualiflyer was in getting the miles transferred to LH, with LH saying there was nothing they could do until the miles were actually transferred to them. Have you checked with Qualiflyer to ensure that they sent the miles to LH rather than to TAP or someone else?

4. I'm not a travel law lawyer, so this may not be viable, but have you tried contacting the U.S. Department of Transportation? I seem to remember that in order for LH to fly into and out of the U.S., they had to agree to DOT jurisdiction on some matters, and the FF program as to Stateside members might be one of those matters. I'd bet DOT could get LH to respond!