So, Bytopia. It's about work; honest sweat and service to the community, productivity and fair reward. In a modern setting, then, there are certainly lots of ways we can interpret that in light of economic theory. Now, something about Bytopia always struck me as the most American of the planes. You've got this pastoral ambience mixed with naked capitalism in Shurrock, the frontier mentality on Dothion. I always thought it would be the plane where serious democracy was most likely to first to take root.
But then, there's also the motto of the plane to labor for your bread, and the emphasis of Dothion... cold, windy, harsh but somehow cheerful Dothion... on the basics of mining and extracting the unglamorous raw material for the crafters elsewhere. How very... proletariat, you know?
So here's my thought. The planes advance in their ways. Bytopia keeps itself productive and relevant, the breadbasket of the planes and the home of good solid craftsmen and mercantile interests. On the one side, you've got labor; on the other side, capital. On Dothion, extractive industries -- mining, oil, and the like... on Shurrock, manufacturing and emphasis on services. And so they develop in different directions. The pre-eminent viewpoint on Shurrock comes to be a collection of representative democracies tending to the conservative and libertarian, with an emphasis on laissez-faire capitalism, manufacturing, finance, and big stretches of rural good-old-boy country farms with 'heartland values' (these, not coincidentally, housing many of the older Powers of the plane). (Unkind observers might note some of the negative traits of these things, sure -- the little guy with less of a share, some narrow-mindedness in the 'values' -- but on the whole, Bytopians are good people, and the plane helps out by its nature with things like environmental effects of manufacturing.) On Dothion, the ideals tend to emphasize community effort and working together for the common good; the governments here are a good deal more socialist and interventionist, taking care of their people and distributing resources where they'll do the most good. (Again, an unkind observer might be uncomfortable with the 'nanny state', or the high taxes, but it's a plane that promises not to run out of resources for the kind of people who come here, that like to work and pay their dues.)
On each side of the Twin Paradises, relations are good-naturedly competitive, but occasionally get a little rougher... across the Pillars, though, things sometimes get downright strained. To prevent conflicts from breaking out -- nobody here really wants that -- a meeting place has been erected, built at one of the mountains and braced on both sides. In the center hall, delegates from the various nations of gnome, halfling, human, dwarf, and others (fleshing these out could provide quite a bit of material) sit in chairs that face each other across the divide. Actually, they are laying down, facing those that seem to be on the ceiling, but the mental attitude is what's important. Here, they come together and communicate, working out their differences and resolving tensions, calmly ironing out disputes and keeping the plane on an even keel.
And I like this too, if only because it's such a great opportunity for plot, plot and more plot. Conflict, intrigue, betrayal - it's all there.
The rule of threes asks kindly for a centrist element across both sides, but may be satisfied in other ways: anarchists don't at all fit, but a Bytopian interpretation of them may work instead. That could, perhaps, be a point of conflict between the two: they may each see centrists as a radical departure from their own views, nearly as much so as the other side.
I'd be more helpful (or detailed) than just 'run with it', but I'd like to see where you'll take it. Or, if you haven't thought that far yet, whatever else the collective wisdom might like to add.