I now have even more information, thanks to the steer Planck gave me.
Save and Autosaves work fine, just so long as I have not come out of OFP, but if I exit OFP, when I come back in I cannot Resume the mission. I get the error message and it crashes.
But:
If I rename the save, autosave and continue files before going into the mission, once I am in again I press escape, ALT TAB, put the filename back to what they were, and it will all then work.
So I don't need to move the files, just rename them, and I don't need to get killed.
Does anyone have any idea what is causing this and how I can fix it?