The problem is still present with 10.8.4 and Toolbox 3.4. Admin account. I haven't tried setting up a non-admin account. I'll try that and see what happens.
If I set up a new aggregate interface such as "Built-in I/O" of built-in i + O, it appears immediately in Toolbox. Likewise if I plug in a generic USB i/f like an iMic it appears, but neither TASCAM USB interface appears in either of the Minis. Unplugging and re-plugging the TASCAM has no effect.
Each Mac had the OS installed from scratch, so there ought not to be any weird extensions in common. The odd thing is, no other app is having a similar problem, including iTunes, Audio MIDI setup, Audacity, Logic Studio, Garageband, Audio Test, or Fuzzmeasure (trial version), nor does there seem to be any interaction between apps.
Your US-800 is OK with the latest software (2.10)?