I am wondering if this gap is too big to tape and mud over. The house is over 100 years old and the walls are not quite straight to say the least. The opposite wall is relatively square btw. It gap is about an inch at the top and tapers to nothing.
I think I'd lay in some half-inch filler and nail on a corner bead, 1/8" from the tile. You'll need to trim the one flange to less than the depth of the gap. Skim the bead out 8-12". This will leave you with a very nice, straight edge that you can caulk or grout the tile to without adding a clumsy visual transition.
I'd lay some sort of filler strip that's the same thickness as the drywall and then put some sort of decorative strip on the unfinished edge of the tile. Even small piece of PVC quarter-round (or similar) would be an improvement.
One option to fill it is to cut one or more strips of drywall that you can get in there. It doesn't need to be perfect, just bring the gaps down to what you can fill with joint-compound.