Here are some suggestions:
Don't use Recycle Backup except for emergencies
Don's suggestion is the easiest to implement, costs no money and will speed up your backups. Recycle backups will take a long time. The main advantage of any backup solution is to backup only changed files. Instead, set the grooming option. I've set my grooming option to keep 1 copy for all my backups because I don't have the space for keeping backup changes and it's essentially the same as a recycle backup. My primary reason for backup is to restore in case of failure and not to store a history of changes. The only time I use a recycle backup is when there is a problem with Retrospect backing up to a media set and I need to start over from scratch.
Try using Retrospect Instant Scan
How much time on the backup is spent on scanning the source for changes? Are you using Retrospect Instant Scan on your sources? Instant Scan will monitor the backup source for file changes. When it's time to be backed up Retrospect queries the client for changes that need to be backed up. It's adds some processing overhead on the source computer when the computer is not being backed up but should start a backup sooner than scanning a source disk for changes at the time of backup.
Create separate Media Set for each backup Source
Having a different backup Media Set for each backup source will allow Retrospect to use backup threads. It will cut down on the "scanning for changes" time because all the backups will be scanning for changes on the clients at the same time instead of: 1st backup scan for changes, backup, 2nd backup scan for changes, backup, etc.
Assuming this is the setup you have now:
You've created 1 media set for the backup destination and set 6 sources to backup to that set. When it's time to backup, only one source will run at a time.
Instead: on your backup destination create a media set for each source located on the backup destination drive. When it's time to backup, Retrospect will start all backups at the same time.
Increase Backup Destination Storage Speed
Increasing the backup destination storage speed will increase the backup speed. It's probably what is slowing you down if you are backing up to a single FireWire drive instead of a Firewire Raid. FireWire 800 tops out at around a theoretical 800 Mbps. Your speed at 580 Mbps is about what FireWire can handle, so even having a FireWire raid wouldn't make much of an improvement. Where are you seeing your backup speed? Is it 580 Mbps or 580 MB/m. The Retrospect console shows MB/m. 580 Mbps would be really fast on a single FireWire 800 drive. You're probably getting 10 Mbps.
The source read speed will also limit the backup. If you are backing up computers whose top read speed is 168 Mbps, and your backup destination can handle 800 Mbps, then you aren't utilizing all the bandwidth of the backup source. This is another reason to create multiple media sets in Retrospect so you can have more than 1 backup happening at the same time to saturate your backup destination bandwidth.
If the Mac Mini has a Thunderbolt connection that would give you the top speed. 10 Gbps. However, the drive connected to it needs to be able to read and write that fast. Leading back to getting a raid. OWC makes a reasonably priced Thunderbolt raid:
If the mini doesn't have Thunderbolt you could try a FW 800 raid:
The more drives you have in a raid the faster the read / write speeds. Thunderbolt is the way to go if you have it.
You can use a disk speed test tool to determine how fast your backup destination disk is. Blackmagic makes a good one that is free:
Even though you are using firewire 800 you are probably not saturating the firewire 800 bandwidth and are limited by your disk speed.