Hi criskcracker.
I encounter this situation quite frequently because I do a lot of edits for other composers and they sometimes send me reworked audio files. So the situation here is quite similar 
I agree with Audioland to save a copy of the Logic project first. Then move the old audiofiles in another folder with a different name, for example “previous files”. This way Logic won’t load them automatically anymore (respectively it would aks where the files are). Then put the new files into the original folder called Audio Files. They must have exactly the same names like the old ones before. Then open the Logic session. You should then have the same regions with the replaced files.
I hope this description is somehow useful. I am not very good in explainig