When I started to chisel off the existing 6x6 tile, what remains on the wall is an utter mess. The tiles are coming off easily enough - sometimes cracking, other times whole.

What remains is a craggy mess of plaster, the material used to adhere the tiles, and holes going right down to what, of all things, looks like cement.
This spot is an outside wall of a house that has primarily plastered wall. Most of the tile is on an inside wall - who knows what's behind that!

The question is, how on earth do I ever get this wall smooth enough to re-tile? A little spackle isn't going to fix this.
Do I chip away all the material to see if I eventually get to a smooth surface? That would leave me with about a 1/4 in indent. Not deep enough for drywall.
What's worse, a small section of the tiled area was just supposed to be painted.

I can use some very tiny tiles that can slightly bend around some larger indentations, but that isn't going to work for anything but the most shallow differences.
Or should I fill what I can and use very large tiles to bridge over some uneveness. This all seems like work-arounds.

Any advice here is much appreciated. Hiring a professional isn't really in the budget.

Thank you.

First: take it all off.

Then: take some good pictures and post them in the Kitchen forum (they do more backsplashes than anyone).