How can I use the file's modification date & time without MDTM or MFMT support?

If your FTP server does not support setting the files last modification date & time (either by using the MFMT or MDTM commands, or via the SITE UTIME command) then SyncBackFree/SE/Pro can change the local source files last modification date & time to match that of the file on the FTP server if that might help (it will not do so by default, but you can select the option "If the FTP server cannot set a files date & time then change the local files date & time to match that on the server" on the main FTP settings page).

See the FAQ question How do you know if a file has been modified on an FTP server? for more information:

SyncBack Touch

An alternative to using FTP is to use SyncBack Touch. SyncBack Touch is a cross-platform file server. It lets SyncBackPro and SyncBackSE copy files to and from another device, e.g. Windows, macOS, Linux or Android device, over the network (LAN or Internet) just like an FTP server. SyncBackFree cannot use SyncBack Touch.

Simply install SyncBack Touch on the device you want to the access the files on and then create a profile in SyncBackPro/SE to use that device.

The advantages to using SyncBack Touch instead of FTP are that you can copy open/locked files, it's far simpler to set-up, doesn't have all the compatibility problems of FTP (e.g. does it support MDTM or MFMT?) and doesn't require complex firewall/router configuration.