It’s called an AB168.

Not to be ugly but your house is surely worth more than $1000. There really is no other path other than a copper snake. QU vs GLD is that it offers pres either local or via DSnake. Very helpful in many situations.

But what are you plugging into the other end of that?

Yes, an AB168 is the minimum you’ll need to connect the digital dSnake protocol with the analog world. As George said, if digital seems to be too expensive or you insist to use the preamps of the desk, a heavy analog snake will be the way to go.
The phrase Media Converter refers to other ethernet carrying media like optical fibers instead of copper, it has nothing to do with “multimedia” or audio.

Both dSnake and USB running digital protocols. To convert analog signals into the digital world you’ll need:
– A Gain stage to adapt analog level to whatever the ADC expects.
– Maybe switchable phantom power to enable use of active DI boxes or condenser mics.
– An Analog to Digital Converter (“ADC”) per channel.
– Some sort of MCU or FPGA to collect digital data from all these ADCs and convert it into the dSnake protocol.
– Maybe some return channels to feed speakers (which again will need DACs and analog driver stages).
– Maybe a rugged case for stage use.

This exactly is contained in a AB168. Building the same DIY will consume time and probably will cost more.

I really doubt you intend to remove the existing preamps and DACs from your desk and stuff them into a box just to spare some bucks.