You need to ask Janome these questions, rather than Fixya I think. The plastic bobbin in the plastic bobbin holder does make a little bit of noise but I don't find it problematic.
Janome New Zealand Limited
Unit 5, 325 Ti Rakau Drive, East Tamaki, Auckland, New Zealand
Providing you are using "Janome" plastic bobbins and are putting them in rotating the right way, as per the little image on the clear cover, there is no reason that the thread cutter should be dislodging the bobbin. When I use the thread cutter, my bobbin turns as thread is drawn off it, but it doesn't move upwards.
Sounds like you have already replaced the black plastic bobbin holder, is that what you mean by "Shuttle"??
My 6500 has had 2 replacement bobbin holders as I keep striking it with the needle during jam ups, which caused plastic burrs on it. On the last service the technician added a little piece that is a janome "after sale replacement" part. It is slightly longer than the standard part, and is a little metal bit on the left hand side of the rotary hook area which seems to be working at holding the bobbin holder in place better. Haven't had a big jam up since he fitted it. But before this, I would dislodge the bobbin holder with a small jam, and then it would just jam and jam until I removed the needle plate with the screwdriver, removed the bobbin and bobbin holder, cleaned out all the thread fragments, then replaced the bobbin holder back into the correct position lining up the two red arrows. Then replaced the needle plate and rethreaded. I learnt to modify my sewing expectations and not try to sew really thick seams as this will just dislodge the bobbin holder again. Jeans hems were always my problem seam, I use a "Seam Jumper" now to handle going from thin to thick seam, and so far, so good.
So I would suggest you ring Janome in Akld and talk to their technical advisor a bit, describing your problem. They may suggest sending it to them for a check out to establish what is going wrong.
If you have trouble describing the issue to then you could always film it with a digital camera and send the file to them.
My only other thought is how you wind the bobbins. It is really important to wind the bobbin smoothly and evenly top and bottom, my 6500 will wind all in the middle if I let it just run, so I always wind carefully and give the thread a nudge with my fingertip to ensure it fills evening top, middle and bottom. But it sounds like you are an experienced sewer and know this already.
I'd say ring Janome and have a chat, I find if you keep your approach friendly and neutral rather than "I've never got on with this machine" that you may get some help from them at resolving this issue.