Hi Joe,
It does sound like the LR Exported jpeg is set to read only. If Photo Mechanic 5 copies the file using the Copy Photos utility, then the new file should have read and write permissions. What version of LR did you use for the Export? Are you using a Windows machine or a Mac?
If Photo Mechanic 5 is not able to update the copied file, then can you zip the original file and post it?
Best regards,
--Bob