I think the varying traffic is caused by varying file sizes. Apparently there are a lot of small files. To use more traffic, you need to copy several files in parallel. The number is specified on the Files tab sheet.
The verification settings are on the tab sheet Comparison->More, so you can take a look there. You don't need any of them for Amazon S3 because all uploads are always checked by MD5 checksum.
If you have small files, the HTTP protocol may produce some significant incoming traffic.
The Amazon S3 file listings are quite big. So if the program retrieves the complete file listing often, that can be a lot of traffic. To avoid it, see below. But this should not be relevant if the program has been running just the one job all day.
Obviously your Internet connection as well as Amazon server availability will cause varying transfer speeds too.
SFFS seems quite slow compared to other file uploads (e.g. FTP).
SFFS can do FTP too, so I really do not know what you mean by this sentence. It's like saying your car is much slower than the highway.
If you are only uploading and repeating the same job in the future, you can save time by using the "Cache Destination File List" feature on the Special tab sheet.