Often a feature pressure of "ship next week" is due to bad management and planning though. Often engineers already foresaw similar needs and were told no before. Then suddenly it is urgent.

my market was exactly this; tied to the start of the semester, if i missed shipping a feature my next shot at getting it used in production was months away. and basically if we missed the fall season it might as well have not even happened.

Ultimately it is yet another optimization problem. You have fixed dev time, a budget and some deadlines. If possible, try rewriting a component and measure the effort and benefits. We had PoC with deep rooted data issues. We knew throwing it away would set us back by a year but it just kept getting uglier by the day. We added a thin data validation API around it which started catching a good chunk of the data issues and let us deploy the PoC. We're now rewriting a new core with built in data validation and tons of performance and reliability improvements.