Recovering from overwatering without immediately repotting everything

I overwatered two plants while trying to keep everything on the same schedule. Their leaves are droopy despite wet soil, but the roots may not be beyond saving. My instinct is to repot immediately, which could stress them further. I'm moving them into better light and airflow, letting the mix dry somewhat, and checking drainage. What signs would make you inspect the roots urgently versus giving the plant time to recover?