You're looking for media server software, specifically software that will interface with the Blackmagic card. On the cheap check out Arkaos, Resolume, Madmapper, etc.,
Another option would be straight playout from Resolve. Arrange the image in quadrants accordingly. Here's is a crude example of how a wide panorama could be extracted from a 16:9 rectangle.
None of this addresses the realities of blending or convergence.
Good Luck
- quad.jpg (643.1 KiB) Viewed 568 times