@Dr. E
As far as I can tell/remember, the only reference in M”B to 6 or 7 re a minyan, is regarding beginning the entire service, not just chazoras hashatz (I think it was around siman 56 or so). But the he, (as well as all poskim) are quite clear elsewhere throughout M”B that one may only begin chazoras hashatz with 10 men able to answer (incl. the chazon himself). Though he does quote a shas hadchak minhag of relying on a child holding a Chumash to make the 10th person.
But, I’d like to stress that the 10-men threshold, is the MINIMUM when one is allowed to start. But even that is not l’chatchilah. Ideally, the chazon should wait for majority (rov) of the minyan to be ready to answer.
~~
Regarding @Sarah S’s original question though, I think M”B also addresses this and says it’s best not to inconvenience others, as @ubiquitin said very nicely.