Just figured out how to do this, if you install the virtual-cam plugin (NOT the built-in one, it has to be the plugin) you can right click on a scene and add a filter. Select the "VirtualCam" filter and select your target camera. I suggest not using the default one as I believe that is the one that the built-in virtual cam uses.
You do have to manually start it by right clicking on the scene, selecting the virtual cam filter and hitting start EVERY time you open OBS, but it still works. I've also notice that it often drops a frame or two when swapping scenes, but that might be fixed if you increased the amount of buffered frames? Also Also, don't select Horizontal flip within the plugin, last I checked that results in it crashing.