> However, the MODX does not appear as a Software Playback device.

Sure, because you can see audio in a SW playback devices (TM FX middle row) only,
when audio came via an application using
- either RME ASIO or
- WDM driver (see driver settings dialog, WDM devices need to be enabled).

As your synth seems to use a driver of its own, most likely no luck.

Eventually you can bring it to work, íf the device would be able to select an RME WDM driver for its output.
But that you need to try out, from my side this is only speculation.

The usual way to record from external devices like synthesizers is
- to have a device with its own D/A converter and
- record it via an analog line input.

One of the reasons why devices like USB micros and other USB only devices are a no go for me to buy.

A workaround might be, to enable the internal soundcard of your PC and connect the output with an analog input of your RME recording interface. Then you have the audio via an analog HW input for recording purposes.

But you need to check whether such a setup works satisfactory in terms of performance / stability.

The recommendet (best practice) way of setting up a DAW (digital audio workstation) is to disable unneeded HW in the BIOS and this is usually also the internal sound card. But if you have a DAW PC which you also use for Office where you might need Skype for business and alike, then you might need the internal sound card still, to be able to connect a PC headset, as these small headsets can not be used on a recording interface, they need a different form of Phantom Power, which is definitively no studio standard and won't be generated for these small headset (mostly condenser) micros that do not need 48V but something in the range of 4-9V if I remember right.