Hi Sally,
What is this piece of Outboard gear?
Why are you trying to do a Mono mix down?

The Babyface only has the 2 analog inputs. The rest are Digital.
You could set Reaper to use the 3/4 headphone outputs as the Main out instead of 1/2.

On the Track in Reaper that has the mono signal you wish to send to the outboard gear make sure the Input is assigned to None.
On this track set the Output to Mono Output 1.
Create a new track Set the Input to Mono Input 1 and the Output to stereo Output 3/4.

You will only be able to use your headphone output for monitoring.
You will also need to rewire things after when you want to use your Main outs for your speakers.

If you really want to use this piece of outboard gear all the time then you will need to get a dedicated external AD/DA to plug into your ADAT/SPDIF Optical I/O.

RME makes stand alone  AD/DA like the ADI-2 and the ADI-8 DS and ADI-QS.
There are also cheaper alternatives from some other manufacturers.
Alternately you could replace the Babyface with the Fireface UCX.
This will give you 8 channels of analog for incorporating external gear.
Cost wise it would be able the same as if you purchased the Babyface and one of the other manufacturers AD/DA.
The benefit would be the sound quality being on par with our higher end ADI series and the extra features or the UCX.

Thanks Chris