Agreed, the DM article does not make it clear that there are multiple instances of JKR - this is an important part of the narrative
However from the BBC article does make clear
During this time, a participant stitched over the Harry Potter author's name.
This implies that one contributor stitched the name which a later participant defaced by stitching over it.
The BBC article further states
The National Trust, who manage the property, said: "The artwork was open to contributions for eight months and closed in November when the piece was finished and put on public display."
So I don't understand it when you say - The NT are upset at someone altering someone's entry on a finished piece of collaborative artwork, I can understand that
Are the NT OK with someone defacing another person's work as long as this happens within their preferred time window but not OK outside this window?
Was the author of the original signature happy for it to be defaced?
Are there any other names on the artwork that were defaced?
When they noticed the defacement, why did they not flag it and repair the damage?
From the description of the project, I would assume that a member of staff was always present when the pubic were contributing stiches (to prevent obscene words etc.) Why was the second contributor ever allowed to deface the artwork?
Reversing the situation
If there were a prominent trans woman's name on the artwork with a black line stitched over it by a third party - would you be arguing that this was done to represent the silencing of the trans community?
I think much more likely that, in the current climate, the black line would be quickly reported to the police who would then investigate it as a hate crime