Thanks!
That's right I stumbled on that Dragon Ball game while looking for similar effects on the SNES. The game has a really nice implementation, I like how it switches from left to right for instance. Also it's much more advanced, with parallax and all the bells and whistle.
I see no reason to exclude mode 0. I think we could also achieve parallax effect with a single background per player, controlling bg scroll with HDMA. Split-screen only uses a single HDMA channel.
The challenge with multiple levels would be determining the relative positions of players, I guess. VRAM wise, each player would have a dedicated tileset. Also, I was able to cut corners (see the look-up tables) by assuming a 512x512 area.
One challenge that I didn't address would be sprites moving from one screen to the other (enemies, projectiles, ...). Since we have the HDMA table at hand, I guess we could just compare sprites positions with the split-point to hide them before they cross the line, but that could be computationally heavy.