All I did for that was swap a bunch of palettes around. The data for the battle backgrounds are kept in a/0/0/7 and a/0/0/8; I'm pretty sure 7 contains the actual battle background itself and palette data for the bottom screen, then 8 contains data for the 'pads' that the Pokémon stand on. I've got some notes that are saying otherwise but I'm pretty sure that's the way it is, from what I just looked through in the data.
But yeah, I just changed the palettes around. Conveniently, the Sinnoh E4/Champion backgrounds are already in the data, you just need to shift them into the correct places.
I can tell you that in 7, Will's background is 212, Koga's is 215, Bruno's is 218, Karen's is 221 and Lance is 224. Their bottom screens are files 259, 260, 261, 262 and 263 respectively. (Note that if you use Tinke, it displays numbers starting from 1, so these indices all appear +1 of their originals.)
In 8, I believe Lance's battle pad is file 46. Not sure about the rest of the E4s though.
It's possible some of the info I told you was wrong; I THINK it's right but I'll let you know if I made any errors.
Also, yeah, changing the wild backgrounds should technically be possible, albeit probably more complicated due to the wider use of colours. You'll have to find the correct palette and edit it (use a program called consoleTool). As for editing the actual appearance of the background, I don't know how to go about doing that currently.