The problem, as usual, being that you are trying to describe something with a term where the common usage is just plain bad faith.
Unfairly attacked?
Harassed?
There’s lots of words…the common usage of cancelling is none of them nor what you described. The common usage is what no one in this thread seems to want to admit. And it’s why the same people who cry about cancel culture want to use it’s supposed existence as a reason to actually restrict others free speech.
But I think I see your point. It's a phrase that can be used lazily and in bad faith and itself contribute to degraded discourse.
It’s important to note that there is a significant portion of the people employing this term in bad faith who are doing now intentionally and to cause confusion. The problem with a new term is that it will, almost inherently, be co-opted by these same groups.
The attempts to mislabel are intentional and coordinated. I think you are coming from a good hearted place, and it’s nice to be able to have this convo, but a new label won’t fix it because the label isn’t the problem the use is.