Playing three RTSP streams, through VLC, casted to television

Question

I have three RTSP-enabled cameras around the outside of my house. I also have a Vizio TV that has "Smartcast" built-in (pretty much a Google Chromecast). I am using the latest nightly version of VLC that allows setting the "renderer" and choosing "Living room" in the list and it will cast whatever is playing in VLC to my television.

Okay, that's all out of the way. I currently have a .bat file that contains the following command:

"D:\Program Files\VideoLAN\VLC\vlc.exe" --run-time=5 --loop --no-video-title rtsp://rtsp-url-for-camera-1 rtsp://rtsp-url-for-camera-2 rtsp://rtsp-url-for-camera-3

This file loads VLC and begins to cycle through all three of my cameras. However, it is showing this on my laptop. What I want to do is be able to load this file and it immediately begin sending this video feed to my television, no questions asked, no buttons to click, just instant cycling of my cameras on my television. On a side note, I realize it won't be instantaneous, but you get the idea.

I found the following command argument to add to the command:

--sout="#chromecast{ip=ip-address-of-television}"

It sorta works. I load the file and it immediately picks up on my TV; however, it doesn't display the stream at all. It just shows the chromecast icon in the center of the TV like it's thinking about showing the feed, but it never does. Then it cycles to the next feed, shows the icon, but never shows anything. And it continues like this ad nauseam.

I'm not sure what the best option here is.. Am I expecting too much out of VLC? Is there a better option available? I also have a "media server" Debian box at my disposal. So maybe there is some software out there that offers a way for me to combine all three streams so that I can have VLC just connect to my media server and stream an "internal" stream that the Debian box is producing, maybe that would be ideal?

I'm not sure where to go from here... Can anyone help?

Edit: After playing around last night, I realized the reason it wouldn't show the stream with the "--sout" argument was because it was cycling too quickly. I set the "--run-time=" argument to be 25 seconds instead of 5, and it worked. The problem, though, is that it constantly has to re-establish the video feed. So there's about a 10-15 second delay in it showing the next feed. It'll show one camera for about 10 seconds, and then that feed will disappear and it'll take 10-15 seconds to connect to the next camera, and then it repeats that way until I turned it off.

So this solution might not be the most elegant to use. Does anyone know of any Debian server-based software that might take these three RTSP streams and combine them into one, so that I can just stream that one URL to my TV and let Debian handle cycling the cameras? I'm thinking that might be the way to go, here.