How can one organise moving a large Q&A community?

Imagine a large healthy online Q&A community hosted on a platform developed and maintained by a commercial company. Suppose that the community is increasingly dissatisfied with the direction the company is going, and feels that its feedback is no longer valued like it was 5–10 years ago. Consider that some members of the community want to organise a move along with all user-contributed content. Whatever the cause, it can happen.

Assuming that legal and technical issues are solved (all user-contributed content is available under a permissive license, database dumps are available, features are similar enough): how could users organise moving to another platform?

For the sake of the question, let’s take a site with 1k–100k visits/day, 5k–50k questions, and 10k–50k user accounts, of which about 1% (100-500) can be considered highly active members.

One historical example that comes to mind is Wikivoyage and Wikitravel, which still coexist seven years after the split.

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