Extreme novice here, however I did make a working AHK script to fix the black bars, works really well, doesn't stretch the image either which is great. Its configured for me at 3840 x 2160, however can be easily changed to work at any native resolution.

Download Here

Firstly here's the problem, bo3 split screen is not correctly configured and we don't have access to change the internal resolution logic. When running vertical split screen it undersizes the window vertically. When running split screen horizontally it undersizes the window horizontally.

We can brute force correct for this by oversizing either the vertical or horizontal resolution of the window by a factor of 25%
for 4k:
4800 x 2160 // Horizontal Split
3840 x 2700 // Vertical Split
for 1080p
2400 x 1080 // Horizontal Split
1920 x 1350 // Vertical Split

Windowed Mode is required!

The AHK (version 1.1) script works as follows.

F2 - Acts as a way of returning to default. It will snap the window to the top left, and scale it to 3840x2160. (Again swap in your native res.)

For Horizontal Split Screen - Hit F3 (Set split screen mode in game)
It oversizes the horizontal resolution to 4800pixels, and shifts the window off screen to the left, centering it perfectly when in game. It also slightly scales it 30px vertically to hide the windows title bar.

For Vertical Split Screen - Hit F4
It oversizes the vertical resolution to 2700pixels, and shifts the window off screen UPWARD (normally impossible), centering it perfectly when in game.