There's definitely a lot of politics involved in such projects. So I've learned that a break is necessary between major engagements to decrease the risk of burnout.

The environment that creates "rescue" projects is usually not one where long term thinking is prevalent. It would be a pet project of someone who's still there or someone who left but where the ultimate decision maker is still there. Either case, you need to walk on egg-shells and be mindful that dealing with the technology problems is the easiest part of such an engagement. I'm not ashamed to admit that I've learned that lesson the hard way.

I was about to ask whether engaging with this kind of people is even worth it. I've seen enough of Jamie Dimon-like power trips to stay away.