A couple of quick thoughts.

1. The two PTZ cameras appear to send their video to vMix PC over your network. Those will be 250-500ms delayed as compared to your Balcony Cam. Network vs. capture card. Capture cards have less delay (aka latency). Using a capture card will eliminate this latency.
2. Any video coming from vMix PC to your video switcher will have more delay than the video coming directly into the switcher. So you may have a lip-sync issue with the PTZ cameras as a result.
3. The laptop can connect to the vMix PC via NDI, so one less capture port is needed.
4. The EasyWorship/Presenter PC can also connect to the vMix PC via NDI, saving another capture port.
5. The PTZ IP controller tends to have some latency of its own. The cameras may take 500ms or so to begin movement after the joystick is moved. You can use one of the X-keys joysticks (XK-68 or XK-12) for the same purpose for about half the price or less.
6. Make sure you follow the vMix Reference Systems guidelines when building your vMix PC or have it built by an experienced live streaming PC builder. Just because a PC technician know how to build a PC doesn't mean they know the intricacies of a live streaming PC.

Hope these are helpful.

- Tom

1. Didn't know the cameras were NDI. Not marked as such in your drawing so I assumed your were using the IP streaming function of the cameras. NDI will work just fine. Expect latency of about 50ms (less than two frames).
2. It's the PC processing of the camera video that adds latency as compared to camera video going only through a switcher. Not sure how fixable it is if you are using these two different methods of routing video. I'd try to take all three cameras directly into the switcher then add a fourth source from the PC for slides, text, graphics, etc.
5. Not suggesting moving the cameras during live, just noting the latency of the joystick. All of my customers that have used the PTZ IP controller complain about the delay in the joystick action.

- Tom