The big rewrite works - but only if you have a team you can trust. You need a new team of seniors to pair with the current team, promise a promotion to the current team at the end of the task.

Committing to an iterative approach is what I do when I don't have enough authority/ political tokens and I can't afford a rewrite.

Over time it gets less and less priority from the business and you end up with half a codebase being crap and half codebase being ok and maintaining stuff is even harder.