How do I route Quartet preamps directly to the outputs? Use my Quartet as an outboard analog preamp?

The Quartet only has ADAT INPUT plugs. There is no digital output on this device.
However you can set up the internal mixer to pass the preamp inputs to the balanced analog outputs. Then you can connect analog cables from the Quartet to the analog inputs of your Symphony Mk1, or other line level input device.

You would need to route the internal Maestro mixers to your analog outputs like this:
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Then adjust your Maestro Mixer 1 and Mixer 2 settings with the mic inputs panned hard left and right. Here's a picture:
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With the above settings, Quartet analog output 3 will only be your signal from Mic Preamp #1, Quartet output 4 is Mic Preamp #2, output 5 only sends preamp #3, and output 6 sends only preamp #4.