There are high temperature paints especially for wood burning stoves. I have not used them, but HERE is a photo of colors available for Stove Bright brand.

Why don't you think about painting the surrounding tiles? We did this in back of a stove and it worked well. It was easier than pulling all the unsightly tile off the wall. To make it disappear, I'd consider the same color as the wall. Don't forget, you can then dress up the corner with your fireplace accessories -- maybe black with brass accents. That will cover up most of the tiled floor if you want to add some color to that area. Maybe a brightly colored wood box?

An inglenook = cozy! It could be wood paneled, or stone, or brick! The problem is black stoves are so visually heavy, to blend it with the surroundings your options are: lighten the stove's visual weight or weigh down the adjoining area with color or texture...