I decided there was no way to rationally deal with this. So I stopped looking at Twitter. That turned out to be the best thing to do. People still said things, but as I wasn't listening it didn't matter. The gossip and malicious slander reached a crescendo as the sale went though, but ultimately had zero impact on what actually happened.
As far as I can work out, what happens on Twitter stays on Twitter, and if you don't pay it any attention it really doesn't matter.
However, the caveat to that is that journalists are on Twitter, pay a lot of attention to Twitter, and report it as reality. Getting dogpiled on Twitter may not matter, but having it reported in newspapers may make it matter.