I'm doing this at the moment. We have a gnarly ball of legacy code that is burning out devs. It actively resists any attempt to disentangle its parts and after years of attempts at refactoring it's gnarliness is barely reduced. I'm of the opinion that the actual problem it is solving is not nearly as complex as the code. We've extracted a smaller problem that contains all the hardest parts and are solving it with 2-3 different approaches. A completely naive implementation of the core functionality took only a few days and is already faster than the original.

The trouble at the moment is convincing the management that a) this is productive work and b) it really is time to (incrementally) rewrite this code - it's beyond saving. From their point of view it looks like we want to scrap something that sort-of works most of time and do all the work from scratch. It's difficult to convey just how much psychic damage the current code is causing to someone who isn't buried in it day-to-day.