Definitely sounds like faulty bulbs. The LEDs ought to consume less power than the halogens they are replacing (which typically consume 20-50W each in GU 10 size), and since you said you can run the fixture with all six halogens installed with no problem, your problem is not simply that six 7W LEDs were too much for your circuit in combination with all the other loads.
See if you can isolate the problem to one specific bulb out of the six by only installing one bulb at a time. It could be a short in one of the bulbs due to a manufacturing defect.