Can a multi-output device have an input?
Ah, I actually found a workaround. My music software (Reason) allows you to wire up the audio output to any channel on the device. Because I created an aggregate with the input and the two outputs, I could split the audio and wire it to the output channels for both the real sound card (for monitoring) and the virtual one (for capture by OBS). It works, and there's no latency.