can we at least admit the possibility that in the instance described by OP the music people simply misjudged the length of the song or the length of the communion line, and somebody got flustered and made a split second decision to keep singing. Sounds like a problem for the priest to deal with in conjunction with the choir, not the concern of anyone else.
Good idea. I used to sing in choirs and singing involved rehearsals, as it would for most if not all choirs. We’d rehearse a song with by singing it the same way every time, so the choir was used to singing, say, 4 verses. Interrupting this during Mass would be chaotic unless the choir was also trained to stop singing at some signal. When a group of people have rehearsed a piece of music, changing it can often lead to a lot of confusion among the people singing.
I read through most of the thread, until I got to this comment to reply, but I’m not sure I saw anyone bring up the issue that some of these choirs are children’s choirs, like the ones I was in, in which the singers are in middle school or maybe teenagers in high school. These are people learning about music and they (at least speaking for myself) - I did not have the knowledge or flexibility of a professional musician, or even an adult. In addition, when adults sing, they are often musically untrained. People without training can be very talented and do a great job, but may have a harder time adapting to change, which means anything different from rehearsal.
Also, to be in a choir, at least for me, meant that people were looking in my general direction and when I was about 12 and singing, I was very self-conscious about this. People who are already nervous are not as adaptable.
It would be a humiliating experience for anyone in a choir, but especially a young person, if the director decided to signal them to stop and the person kept singing b/c that’s how they’d rehearsed it, but they were singing when they shouldn’t have been. That’s the kind of thing that I would have had nightmares about.

It can make a sensitive person, especially without musical training, leave the choir and not come back.
I think a good solution is what several posters mentioned. Have the choir receive first, which can be done very quickly, and then have everyone settle in and start singing. Then it’s not a distraction and the priest doesn’t have to wait.
If the choir is used to singing while some members are taking turns to receive, that works too, assuming it goes well with the music being sung. But that would need to be discussed with the choir in advance and may require some practice. Once people got used to it I imagine it would be fine.