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I don't think rsync searches for differences smaller than an entire file, just compares checksums and replaces.

Check if your FTP client has a batch mode, that may avoid it prompting for local file names. It might be -b, not all ftp clients are the same.

Try ls -l filename which may work in some ftp servers. You may need to do that in a different ftp <<END_SCRIPT block so you can save its value to process it into something you can use.