The easiest setup would be to use the calls as is in vMix. Add the callers to a Bus like now and send that bus output to your audio desk. Create a mix minus at the desk that includes everything but not the calls and input it into vmix. This way vMix uses the callers natively, and you can use them for the radio, and you get the audio from the desk to be used in streams and records.

I guess the delay isn't that much finally. Have you tried to enable NDI on the output and insert that as a source (attention of a possible loop). The NDI is already a bit delayed at my end. If that isn't enough you can further delay the NDI in the advanced input settings.

NDI the video of the callers back in - you can delay that (on the settings of the input > Advanced, choose a frame delay and hit apply). Every caller is available as an NDI source if you turn it on the global vMix settings.

Enjoy the absolute wild fun that is figuring out how delayed the audio is compared to the video! You can only adjust by whole frames in the video delay :)

There is currently no built-in video delay for vMix Calls. However, there are a few workarounds that you can use to achieve a similar effect.

One workaround is to use a separate video delay device. This could be a hardware device, such as a video switcher or delay unit, or it could be a software application, such as OBS Studio. Once you have connected your video delay device to vMix, you can route your vMix Calls input to the delay device and then route the output of the delay device to a vMix Input.

Another workaround is to use a virtual camera. A virtual camera is a software application that creates a fake video feed that can be used as a source in vMix. There are a number of different virtual camera applications available, such as ManyCam and OBS Studio. To use a virtual camera to create a video delay, you would simply need to route your vMix Calls input to the virtual camera and then set the delay on the virtual camera.

Here are some specific instructions on how to use OBS Studio to create a video delay for vMix Calls:

Open OBS Studio and create a new scene.
Add your vMix Calls input to the scene.
Click the "+" button in the "Sources" section and select "Video Delay."
In the "Video Delay" settings, set the delay time in milliseconds.
Click "OK" to create the video delay.
Add the "Video Delay" source to the scene.
Click the "Start Streaming" button to start streaming the video delay to vMix.
Once you have started streaming the video delay to vMix, you can add the "Video Delay" input to your vMix production. You can then use the video delay to create effects such as replaying highlights or delaying the video feed to match the audio feed.

I hope this information is helpful.