The command cp -P doesn't apply to your needs. You are using uppercase argument letter -P which is used to never follow symbolic links.
What you want to use is lowercase to preserve timestamps: cp -p
As described in the comment section of the question, using the correct gid and uid solved the problem:
sudo mount -t cifs //mynas/folder /home/mnt/nas/ -o user=username -o gid=1000,uid=1000