I've heard another story regarding the Strzok "reassignment": that the anti-Trump texts exchanged with his mistress were uncovered by the ongoing inspector general's investigation of the FBI and DOJ, and when brought to Mueller's attention, Strzok was relieved of his position in counter-intelligence and demoted to the FBI's HR Department. I buy this only so much: Mueller must have know Strzok was anti-Trump - Mueller only hired on people who were anti-Trump - so that fact must have come as no surprise. But I do think the IG investigation uncovered something - something big enough to bust the top FBI counter-intelligence officer down to HR. What that might be remains a mystery for now, but it was certainly something more significant than anti-Trump texts with his mistress.
“Mueller must have know Strzok was anti-Trump - Mueller only hired on people who were anti-Trump - so that fact must have come as no surprise. But I do think the IG investigation uncovered something - something big enough to bust the top FBI counter-intelligence officer down to HR. What that might be remains a mystery for now, but it was certainly something more significant than anti-Trump texts with his mistress.”
I agree with your first point, Mueller had to have known Strzok was anti-Trump before he joined the Mueller group.
There is no evidence whatsoever that Strzok was “busted down.” There is no official report of any disciplinary action against Strzok. When it was announced it was said it was a transfer and no reason was given.
My thought, and this is only speculation, is that by July there was no more investigation to be done by Mueller. The Flynn interview had already been completed. The Manafort accusations were simply based on activities from several years ago when Manafort was working with Podesta and probably Clinton.
However, the DOJ and Congress were starting to investigate the FBI and asking for records related to the Clinton investigation, Fusion GPS and the infamous phony dossier. Strzok was probable needed in FBI HR department to hide, destroy and falsify documents and personal files and impede the investigations.