The list of rabbis who hold it’s assur might be even more impressive, but of course, they don’t publish it.
To give some credit, they do allude to the fact that they were unable to receive endorsement from some rabbis. They claim that most who wouldn’t endorse it were for “non-halachic” reasons. If that means zilzul Shabbos (which I don’t see a way around, and their rationalization is a bunch of empty words), I would call it halachic. They could use the term Rabbi Oelbaum (who strongly hinted that he holds it’s zilzul Shabbos) used, and say that their lack of endorsement was not for melachah reasons. Even this is far from clear (and they hint that some asser for melachah reasons). The miskaven issue is difficult to get around.
If you look carefully (to be honest, I looked at only a couple), at least some of the “endorsements” are pretty tepid.