Here's a mock-up:
And for attacks where one Pokemon is getting hit, my plan is this: the two Pokemon that aren't in the fight would just fade out temporarily (with a palette-based effect/animation) before the attack, then the other two would center themselves so the attack animation would work as intended; the attacked Pokemon would then take its damage, and then these two would return to their usual positions and the other two would fade back into place. This way, there won't need to be different animations depending on the positions of the Pokemon, which will keep things from getting too unrealistic.
Also, the HP bars are 16px smaller for space reasons, but I would imagine that could be easily overcome, and that making a new HP bar just for double battles shouldn't be too much trouble.
In the case of contests, that's fine if it hasn't been implemented. I won't need to do anything with that right now; it's not a big deal.
Absolutely love that Mockup. I'm sure with some scripting it could be easily accomplished. The font however I'm not so sure about @__@ The GSC font has always struggled with me, along with the Essentials textbox since I can't force it to display two lines at the correct height.