I have recently been the primary organizer and lead author on a large-scale collaboration, in my case an inter-laboratory study that took place over two years and with more than 100 contributing teams.
The paper has been accepted and is currently in press, and my experience so far has been actually a remarkably low amount of pain. The way in which we organized the study and the subsequent writeup had very clear roles, so there was never any question of having 600+ people trying to collaboratively write up a document. Instead, I led the writing with help from the other core authors; once we were satisfied with the draft, we circulated it to the whole community of authors for review, consent, and corrections, with a one-week deadline for responses. Lots of small corrections came back: we integrated them and submitted the paper as planned.
With all of those eyes on the paper, it is perhaps unsurprising that the reviewers requested only truly minor revisions, which meant there was no need to involve the entire community in the revision, just the core authors. A live-updated draft has always been available to the full community, however (Overleaf is great for this purpose), and additional small corrections have continued to trickle in, up to the very final revision.
In short, then, we simply short-circuited the challenge of many authors by using the project organization to divide into a small group that managed the actual writing of the paper and a much larger group that gave advice and consent. There was one very busy week while the bulk of the feedback was coming in, but other than that it has not been very difficult to manage the paper-writing process in the least, and it appears to have been a good experience for all involved.