I went with great circles since that feels like the most “natural” straight line on a sphere — the path you’d walk if you just kept going forward without steering. You could define "straight" as a constant compass direction (I think it's called a "rhumb") -- that would look straight on a Mercator map but would actually require regular steering adjustments to maintain the bearing.
The other methods are about defining different meanings of what "going around" actually is while constant latitude is a special case of many such methods, e.g. great circle, not a new definition of what going that way means.
