I think a natural stone tile is a great idea - something matching your floor would be nice (possibly the same tile, but smaller). If you are doing the work yourself, you don't necessarily have to remove the four inches of backsplash. Here is a kitchen I tiled in Century City a few months ago:

I always wanted to do a stacked stone but was worried about how hard it would be to keep it clean behind the stove/oven. I love the idea of using a stone but need more details/ Please tell me what size and color you would recommend,

I really don't want to remove the 4" soapstone back splash.

Very pretty kitchen! Do you like penny tiles?

I have heard warnings here about keeping stacked stone clean. However, my own backsplash doesn't get that dirty. It was just painted wall, recently tiled. Perhaps someone with a stacked stone can give you some help.

In the picture posted by Wacky Workshop, both the cabinets and countertop have no movement, allowing for a busier backsplash. Since your cabinets are wood, I would stick to more muted color tones and a simple pattern - possible as I posted above, 3 x 6 subway tile style. I did see similar in a smaller tile that was attractive too. I almost used it in my wood kitchen, but then changed my countertop choice and that changed my tile choice.

Designers will recommend removing the four inch splash and it is usually not hard. However, the rest of the world doesn't know it "should" be removed. Do as you are comfortable with:)

As long as you use a good sealant, stone tile is not that hard to keep clean. If you are able to keep your stone floor clean, it shouldn't be that different around your appliances ;-) The beauty of tile is that it is an art that allows you to express yourself. I have used tiles that were one inch square up to a foot square for backsplashes. For your kitchen, I would suggest the lightest color from your floor or even the same exact tile because the orange tones will enhance the warm wood cabinet color. Instead of just a square grid pattern, putting the tiles in a diagonal diamond pattern will be a nice effect. :-)

Great looking kitchen. Do you like any of these? The diamonds are actually slate like your floor and the dark gray ones will bring in your soapstone. The 3rd one is Thassos and marble since your husband like the white. The gray tones in the chevron will also bring in your countertop. The hex mosaic is a combo of of carrara and other natural stones.

I'd look for a mosaic slate in the same coloration as your floor tile, and I WOULD remove the four inch splash for a good looking install. The change in scale, but repetition of the tones would look lovely and avoid the busy effect. I'd keep it square as the flooring. Similar to below, and check first that your floor tile may have a mosaic match......you may use a floor tile on the wall, just not the reverse with wall tile on a floor.

http://www.homedepot.com/p/Merola-Tile-Ardesia-Slate-12-in-x-12-in-x-6-mm-Porcelain-Floor-and-Wall-Mosaic-Tile-WTCARDSL/204787031?cm_mmc=Shopping%7cTHD%7cG%7c0%7cG-VF-PLA-D23-Tile%7c&gclid=COOx59_arM4CFQ6TaQodivoMiA&gclsrc=aw.ds