I have never seen them take the oyster shell. A small tin of it disappears over months, so perhaps some of the birds are taking some and some aren't? I'm not sure.
As far as boredom goes, my wife and I have done a lot of research and talked to folks about the required space and realize this is a controversial topic and everyone has an opinion and different experiences. We believe our birds should have adequate space to not be acting in this way, but agree 6 birds is probably pushing the max, and we concede that many other factors will affect boredom as well, not just space constraints.
So as an experiment... try crushing up some oyster shell so it's fairly fine, and mixing it into their feed. Add it in 2-3x a week for 2 weeks. If there's any improvement on the shell quality in that time, that tells you they're not eating the oyster shell (at least not enough to help).
I do have to regularly supplement extra oyster shell for one of my birds as she will not eat it on her own.
As far as the space issue, I'll say some of it has to do with individual birds. Some might be pretty tolerant to confinement and behave well even if you have less than ideal space. Others are the complete opposite, and if they're upset at close confinement, their behavior can affect the others - imagine if you had a roommate that was just stressed all the time and acting up, it'd make you stressed out too. Chickens need stuff to do, to keep them busy, so they don't have a need to pick on one another to relieve stress. But "stuff" takes up space, so it's all tied together.