In your VOIP sofware, set input to the master input or master mix channel. Now its input will be the sum of all of your outputs that are set to record.

In Reaper, set your track's output to the physical channel that you have your mic plugged into instead of sending it to the master. In my case, I use Channel 1.

Now set Channel 1 (or whichever channel you're using) as a USB return, if you have such a button. On the Soundcraft Signature MTK boards, you'll find the USB Return button for each channel located just underneath the gain pot (the topmost pot on each channel strip). On any channels that have a 100Hz roll-off feature there are two buttons beneath gain, USB Return is the one on the right.

Once the routing has been taken care of, arm the track that's taking its input from your mic (F7) and set monitoring to "normal" (F8).

Make sure Reaper is using ASIO and that sample rates match everywhere.

That should do it!

Kudos to Seve Nutt for writing this up, and a hat-tip to Patrick Perdue for showing him the ropes.