I have a 6600 that I have had for 4 or 5 years. I never worry about the thread I use in it. I use everything from cheap walmart thread to Aurifil in it and it does just fine. I have had to adjust the bobbin tension when I wanted to do bobbin work using metallic thread.
Are you putting the covers on the thread? Those little disks that go on top of the spool pin after the thread.
You may have a cracked bobbin case. Or, have you had the bobbin case out and got it back in wrong? I use Janome, Babylock and Dritz bobbins interchangeably in mine with no problems.
Finally, I was at a retreat a few weeks ago and a woman asked me to come trouble shoot her 6600. She had the bobbin in backwards. Did not know it went a specific way and hadn't paid any attention to how it went it.
Recheck every step of threading against the manual. Don't mistakenly take the thread through the bobbin threading on the top.
I agree with going through lessons at your shop. If they can't make it sew right with your thread, it may very well be a lemon. I still think there may be a crack in the bobbin case.
I am so sorry you are having these problems. I consider the 6600 a workhorse and it is my favorite modern machine I own. Never gives me a lick of problem. I service it myself and I clean it after each project.