We get this as well with multi crew line training sort of. There is huge debate if to log it as co-pilot or PICUS during company conversion as a DEC.
I just log it as Co-pilot can't be bothered... PICUS is just a construct to allow zero to heros to get enough PIC time to get a ATPL. After you have an ATPL then its pointless. Someone may suggest you log it as PICUS.
Personally if I was you I would log all the flights and put in the remarks col. Company conversion line training up to you if you if you get the person to sign each one off.
Then don't bother adding any of the hours to your totals. With 9000+ hours they are not going to do anything realistically for your CV as single pilot PIC. The only thing I can think of that requires MEP SEP pic time is the entry requirements for MEP CRI class which you need 30. If you have more than that anyway your not loosing anything.