Thanks for the explanation, WanderingJim!
Part of what prompted me to think of that possibility was the section below from the Inyo website. It seems to say that it's okay to enter/exit/re-enter as along as you don't exit for more that 24 hours. But maybe I'm interpreting it wrong.
(from
https://www.fs.usda.gov/main/inyo/passes-permits/recreation)
Crossing Park Boundaries
Your wilderness permit must be issued via Inyo National Forest if your trip starts from Inyo National Forest, even if the first night of your trip will be spent in an adjacent national park or forest.
One permit is valid for the duration of a trip, including traveling through adjacent parks and forests.
If you exit the wilderness in Inyo National Forest for more than 24 hours or re-enter at a different location, a new permit is required for the new entry location.
