OP is stuck with four triangles along a bevel on a sliced UV sphere, and wants the principles for fixing edgeflow, not just this one mesh.
The setup: A 32-vertex UV sphere, sliced with a knife at an angle, with leftover vertices removed, then the edge beveled.
The problem: Four triangles appear along the bevel, and OP wants an all-quad mesh.
The fix tried: A loopcut running from the subdivided base of the triangle. It removed the triangles but brought shading errors, which OP admits make it imperfect.
The real issue: A smooth solution found after an hour of noodling couldn't be rebuilt the next day, from the same shape and dimensions.
The shape is easy to repeat. Remembering the route is the hard part.
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TL;DR of the post, generated automatically.
OP is stuck with four triangles along a bevel on a sliced UV sphere, and wants the principles for fixing edgeflow, not just this one mesh.
The shape is easy to repeat. Remembering the route is the hard part.