This article pointed to a few cases where people tried to do the thing, i.e. the pledge taken by individual researchers, and the requirements placed by certain funding channels, and those sound like a solid attempt to do the thing. This shows that people care and are somewhat willing to organise about it.
But the thing I don't understand is why this can't happen at the department level? If you're an influential figure at a top-5 department in your field, you're friends with your counterparts at the other 4. You see them in person every year. You all hate $journal. Why don't you club together and say "why don't we all have moratorium on publishing in $journal for our departments?"
No temptation for individual research groups to violate the pledge. No dependence on individual funding channels to influence the policy. Just, suddenly, $journal isn't the top publication in that field any more?
I'm sure there are lots of varied reasons why this is difficult but fundamentally it seems like the obvious approach?