|We use a solution from Nuance (NSI) called Output Manager to achieve exactly this, for a similar number of MFPs. We optioned it as part of our MFP contract, it might be worthwhile talking to whomever handles the printer contracting to see if you have access to a tool like that as a part of the contract itself.
If you guys use Scan to Folder, you might already have a tool that can be configured for this purpose.
"Never attribute to malice that which can be explained by stupidity."
- Hanlon's Razor