Actually, since this isn't really Pixel Art (it's a matter of definition, but to me, Pixel Art means you place each pixel using a fixed, low color palette), I'd go the "draw it at a high resolution, then scale it down to 320" route without using nearest neighbor scaling or a limited palette.
There's a clear benefit to doing a low-res game, but there's no obvious reason for downgrading art to a 256 color palette. It servers no purpose unless you actually do a 256 game because you want color-cycling (sacrificing transparency in the process). Also, the method you've used is flawed; the dithering is too uniform and there's noise in the picture everywhere (color noise near dark parts, and artifacts in the white parts).
There's also a big difference to the Indy3 backgrounds: black outlines.
My point is: since you aren't even trying to copy the Indy3 style 100%, why stick to its limitations? I'd either try to recreate the rather beautiful background art of Indy3 or, failing that, use 16bit backgrounds.
It's pretty much impossible to create something that looks like Pixel Art without actually pixeling it.