Hello Phantasmic Fox,
I'm not quite sue by what you mean by - quote - "The order, by any means, remains as so: earth is as to water is as to air is as to fire, or fire is as to air is as to water is as to earth?? Can you explain that please.
You ask how others place air and fire and why - so here's how I work with the elements
Earth - elemental - Gnome; direction - North; season - Winter; time -
midnight; colour - green or black; cold and dry; Feminine; rules solidarity, material things, the body,
Air - elemental - sylph, fairy or hawk; direction - East; season - Spring;
time - dawn; colour - yellow; hot and moist; Masculine; rules thought, wind, intelligence
Fire - elemental - salamander or dragon; direction - South; season -
summer; time - noon; colour - red; hot and dry; Masculine; rules strength and passion
Water - elemental - undine or mermaid; direction - West; season - autumn;
time - dusk; colour - blue; cold and moist; Feminine; rules the emotions
When casting the circle I place Earth in the North of the circle, Air in the East, Fire in the South, Water in the West and Earth in the North.
There was/is controversy over where Air and Fire should be placed - some traditions place Fire in the East and Air in the South. MOST practitioners, groups and covens place Air in the East and Fire in the South. There was a story going around that, years ago, the Golden Dawn put out a blind mixing the placements of Air and Fire so there would be confusion - which there is, of course.