i dont know much about P2 (correction, i dont know ANYTHING about P2!) so maybe you dont need this info…
but to do this with MM:
use MOVE mode
DONT delete unused
Base Media File Names on: CLIP NAMES
BROWSE to a location on the SAME drive the clips are already on.
when you hit OK,
the clips will be moved from the folder they’re in to a new folder:
Nominated Location/Media/Project Name
and the files names will adopt the clip names in the process.
you wont get, or need, a new project.
the clips will go offline in your current project, but then reconnect.
warning: clips already in the timeline may nor reconnect,
and you may need to reconnect them manually, one by one.
cheers,
nick