Exactly the same problem here! (Amsterdam). We've only 1 laptop HP 550 for private use. The laptop has been 4 times (!) picked up for repair. The service of HP is very good, I notice. Just give a call to the HP global support number and often the next day UPS is at your door to pick up your laptop. You don't even have to pack the laptop yourself. Return is often in few days as well. In the case of the Netherlands, they sent it to Polen! This was the good news. The bad news:
4 Times sent away for repair is very anoying. UPS demands that you stay home between 08:00-17:00. The HP helpdesk is not very competent. They just go into the scenario: Did you do this and that? Of course a firmware update is 1 of those steps. It doesn't help. After first time pick up the display was renewed. Few days later the second repair the inverter was renewed. The third time repair the display was again renewed (?!) cause the helpdesk stated that I should have a guarantee of the 3 months on the first repair. After a few days the laptop came back and still the flickering problem there! With the 4th repair they changed the battery cause I noticed and told the helpdesk that the problem occurs while working on battery. But after the 4th repair, still the problem was there.
After that I was tired of it and wrote a complain letter to HP Customer Relation Management by email attachment. Already 2 days later they offered me a new model laptop with at least the same spec as the initial one. They offered me a choose of 2 and choosed for the HP Probook 6540b (WD683ET). This model is way better quality than the 550! Double price as well. So now I'm content with this solution and service in spite of the anoying period before.
What is quite stupid is that HP this display flickering problem doesn't identify as a world wide known problem. The helpdesk doesn't know anything about this issue and should read this topic. Or at least Googling on "HP 550 display problem".
BTW: What are your results so far?