The thread head is really supposed to "mean" how would Kathy spin Futures End when she had to tell Temporal Investigations, but there's even the possibility that Janeway could have decided to keep quiet.
But there's not just a question of Janeway keeping Quiet. There's a 150 people on board writing personal logs and duty logs that at any moment could just have a stray reference, or there could be an outright whistle blower who believes that this is too big a secret for Janeway to control. This means that Janeway (Tuvok) would have to read and edit every log produced by the crew for the next FOREVER to control the displacement of information.
You do understand stand that by creating such a conspiracy that Janeway becomes complicit and an accessory to everything that Braxton and Starling did during the course of Futures End?
The alternative is that the Federation has to blow up Earth themslves in the 29th century to trick Braxton into going back in time to preserve causality as they understand the theory badly.
By actually blowing up the planet or by forcing false memories into his head I'm not sure, it really depends on how hard the guy s in charge are in the 29th century