Drywall Gap Too Big To Tape
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.