To be honest, the problem with external capture devices is the interface bandwidth in between the capture device and the computer. USB3 can only do 4k@30, Thunderbolt 3 can handle more, but there's only a handful of devices that support that, and those devices only support a single input.
Here's another method to get this working for you on a mobile setup, that doesn't involve outboard camera switchers:
If you don't need 1080p or higher resolutions for each of your cameras (outputting to led walls with actual pixels in the 720p range, or you don't mind up scaling), you could use this device:
http://decimator.com/Products/MultiView ... _Quad.html
Or this one, if you want a viewer:
http://lilliputweb.net/a12-lilliput-12- ... h-sdi.html
to take in 4 sources (the camera's I listed earlier are still my go to choice for on stage cameras).
From here you would send out a single 1080p signal to a capture device (I like Magewell and AJA) and then inside Resolume you could do a little magic.
You would add this capture device to it's own layer and then bypass the layer, then inside advanced output you could add 4 screens and set each of their slice inputs to the layer with the capture device and then resize the input slice to fit one of the 4 cameras, repeat with a different camera choice for each of the screens. (breaking the screen into quads). Be sure to un-check the two tick boxes at the top that involve layer opacity and bypass, this will prevent the quad view to come through to the composition.
Now put those 4 screens at the bottom of your list and set their outputs to Spout, then create a new screen and put it on top and set it's input to composition.
Close out of advanced output and add 1-4 new layer and add your 4 Spout input devices (the screens you just created) to one or all of those layers.
You now have a 4 camera switching system.
Be sure to set your original capture device clip to "Persistent" and always keep it on.
Your camera input resolution will be 960x540 if you're using a 1080p composition.
From there it is being resized to a 1080p output (2 times up scaling)
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If budget wasn't an option, I would just use a desktop with a 4-8 input capture card (AJA, Decklink, Blackmagic)
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Here's a video demonstrating the method (layer 1 is acting as my input capture card, it's just a test card though... Same principle applies):
You can use outboard camera switchers as well if they give out a quad view.
If you are interested in the Decimator, Shoot me an offer and I'll sell you mine. I used it on one tour and its been collecting dust in my pelican case ever since.