Wow, thanks for the input everyone, especially the photoshoppers!
I initially thought about porting over the Wonderswan backgrounds with size adjustments. But we can do better than that and here's why:
The WSC version uses one 16 color palette per background. The SNES original uses two 8 color palettes. My hack expands this to two 16 color palettes. Minus transparent colors that's 30 (though transparents can be used as black - Square did).
The tricky part is the tile limit. The most tile intensive background is the field one. That one uses 40 8x8 pixel tiles. That space is always reserved for bg graphics. If I managed to move some things around, I think that could be increased to 63 tiles. That's what the game engine can address without having to be rewritten.
The version I'm particularly interested in for backgrounds is the mobile version (including After Years). The screen size is closest to the original and it seems somewhat simpler than the Wii version. Sadly, there doesn't seem to be a tileset of the mobile backgrounds anywhere...
Of course none of that could hold a candle to what Granville did.
I'd like to see a similar version of the beach... What software did you use?
P.S. I ripped off Rudra No Hihou for the desert ground.
My apologies for not explaining what I did to get these images. I didn't want to assume it was possible to insert them into the SNES version.
I don't deserve any real credit or praise for what I did. It was a VERY simple and automated process to resize and reduce the colors, no skill or photoshop required whatsoever. You could do it in under a minute yourself for each background. All you need is Irfanview (and there are probably other programs that offer the same/better functions), and this sheet of the PSP battle backgrounds-http://www.spriters-resource.com/resources/sheets/48/50889.png
Each of the backgrounds when separated seem about 512x304 each in resolution. Separate one of the backgrounds from this sheet and open it in Irfanview. Under the "Image" menu, there's a Resize/Resample tool. Before using it I also checked the options to preserve aspect ratio, as well as the Lanczos resampling filter and "Apply Sharpen after Resample" option. I then resized the image to 256 pixels wide (preserve aspect ration automatically detected the proper vertical resolution as 152). Hit ok and you're already half done.
After resizing, find "decrease the color depth" under the "Image" menu. Here I checked "Use Floyd-Steinberg dithering" and "Use best color quality". You can select a custom amount of colors up to 256, so you can use as many as the SNES can handle. I tried 14 to match the original SNES colors, 17 to match what it appeared the Wonderswan version handled. And then 25 like your edited desert scene. The exact palettes required by the SNES may differ from what Irfanview uses, though it may not be too hard to swap them with whatever SNES requires.
Incidentally, there's also a submenu under "Image" in Irfanview called "Palette", and another menu called "Edit palette. You can use this to view and even manually edit individual colors of an image if it's 256 colors or less. I didn't use this in the process other than to determine the quantity of colors there were in the battle backgrounds for the original SNES, Wonderswan remake and your own edits.
Here's the same process applied to the beach scene using 25 colors (the dithering used for the sky gradient could possibly use some more manual tweaking, might fiddle and see what it looks like)-
EDIT- I don't know if this is any better or not (not very good at image editing this sort of thing), but here's my attempt at trying to clean up the sky dithering a bit for the resized beach scene above-