video capture card with 1600 x 1200 resolution support.?

1600 x 1200 is not normal video, it is VGA or some Game machine format. ATSC is only 480, 720 or 1080 scan line. perhaps what you are calling a video capture card is really a screen capture card. that is a very different thing, and should not require you to get a separate device, it would be an app, possibly one you could download for free.

It probably will work at other resolutions, however not with any kind of display that is greater than 1920 pixels wide OR 1080 pixels high - which is where you are having your issue.

*I've a different brand and it'll capture pretty much any resolution which is lower than it's maximum, but then only saves to one of it's preferred formats.

So it's likely that you'll need a 4K capture device in order just to get that 1200 pixel height - or just find a resolution where the height is lower than 1080! My advice would be to get a discrete device though - one that saves either directly to a USB memory key or to an SD card (and you'll need a device with a large memory). Your problem at the moment is the lack of these from the big name capture companies - so you may well either have to wait, or just drop that screen height below 1080!