Cut vs patch plaster and wire mesh
Your plan seems sound enough. You are right that joint compound and spackle are not the right material for your upper fill.

I would not cut down through the wire, but would cut to the depth of the wire in a straight line across, which should leave you a fairly uniform depth. Then use a piece of plasterboard to fill the area up to the corner, fastening your corner bead over it. Use plasterboard as close in thickness as you can but not over (under is better than over).

Then use successive coats of patching plaster or joint compound to match surfaces, feathering way back over the existing plaster and sanding smooth.