A lot of cheaper "4-input" cards have only a single converter, and a 4-way switch to feed that converter. That's what makes them cheap. They're fine for security, but not for us. If that's what you have, then you can't ever have two visible at the same time; not even during a transition. And you probably can't even cut nicely either, as the same converter needs some time to re-sync to a vastly different signal.
Googling what you have tells me that you don't have that, but what you do have is grossly overpriced for a set of functions that OBS already has. You can probably sell it (used now) and buy a 4-converter (not just 4-input) card, entirely with the proceeds.
Acasis PCIe capture card supports multiple HD resolutions (such as 4K60Hz), bringing crystal-clear visual effects to the audience. It also supports quad HDMI or SDI simultaneous input, allowing you to flexibly adjust between different camera angles or input devices. Solve your professional video...
www.acasis.com
At any rate, I think the problem is best solved with a capture card that does indeed have a separate, dedicated converter for each input. Or a set of single-input cards that all play nice with each other.