Have you tried rsync?
Thank you Steve! Well, I have now. Error output as follows, after a test transfer of a few files from one of my FAT32 partitions to the NAS using grsync. I set the option 'preserve time' in the Basic options tab.
rsync: failed to set times on "/mnt/backups/New Folder/.": Operation not permitted (1)
rsync: failed to set times on "/mnt/backups/New Folder/.AR Text 140410 - sent to TM.doc.F9Jzab": Operation not permitted (1)
rsync: failed to set times on "/mnt/backups/New Folder/.SPAR Annual Report 09-10 edit imogen 200410.doc.1NVvK8": Operation not permitted (1)
rsync: failed to set times on "/mnt/backups/New Folder/.SPAR Annual Report 09-10 edited World Tree.doc.nHGzr6": Operation not permitted (1)
rsync: failed to set times on "/mnt/backups/New Folder/.SPAR Annual Report 09-10 instalment 1 engagement.X3xve4": Operation not permitted (1)
rsync: failed to set times on "/mnt/backups/New Folder/.SPAR Annual Report 09-10 instalment 1 engagement.doc.DESX71": Operation not permitted (1)
rsync: failed to set times on "/mnt/backups/New Folder/.SPAR Annual Report 09-10 instalment 2 edited World Tree.doc.iRXU5Z": Operation not permitted (1)
rsync: failed to set times on "/mnt/backups/New Folder/.Styleguide 31.xls.mUw5aY": Operation not permitted (1)
rsync error: some files/attrs were not transferred (see previous errors) (code 23) at main.c(1042) [sender=3.0.7]
i.e. looks like I have a Samba permissions problem of some kind.