I was recently looking for a FREE backup utility and after visiting several sites that I frequent for programs I came across Cobian Backup. http://www.cobiansoft.com/cbnew.htm
Granted I've not yet had the time to sit down and read through the help and learn the program, but this is the eleventh version of the software and the NEW features listed are below. Looking through them I see several that seem to meet your criteria. I'm just not sure, yet, whether it meets all your criteria. But I'm sure it's worth a look!
** New Features for version 11*
Welcome to the new version: Cobian Backup 11, Gravity
- AES encryption (128, 192 and 256 bits)
- The directories Settings, Logs and DB can now be configured manually
- A task has now the Priority field
- A new scheduled type is added: On startup
- A new scheduled type was added: On first Monday, On third Tuesday, etc...
- Now you can limit the number of Differential backups as well
- Now you can select a fixed day of the week to make an incremental or differential backup Full
- The program can now automatically delete old files
- Suspend and Hibernate are now Events
- Sources and Destinations can now be sorted "As Explorer"
- Delete empty directories is now a Task property
- A LOT of new parameters can now be used (see the help file)
- The task list can now be divided and organized in groups
- Inclusions and Exclusions can now be arranged
- The Deleter can now delete multiple sources
- The Safe Mirror directory keeps now the original directory structure
- You can now link tasks as an event
- The installer is now improved
- The application can now be closed from every possible desktop
- Old encryption methods are now deprecated
- The decryptor and decompressor accept now multiple sources
- The decryptor and the decompressor accept command line arguments
- The program checks the existence of the destination file even when using the attribute method
- Counting files can now be paused or canceled
- The body of the mail is now configurable
- The Remote Manager is fully rewriten and can now show the progress of the remote client
- The Remote Manager can now get the FULL log file of the client
- Restart and Shutdown work now even with impersonation
- Missed backups don't restart or shutdown the machine now if that event is present