You keep using this word hemiplane, but wouldn't the northern bit of the flat earth only be a quarter of its area? Or are we going to condense the lower latitudes and stretch Australia out even more until it looks more like Japan?
As for the differences in the north and south winters, is
this what you're talking about? This came up in another thread and the upshot is that seasons are driven almost entirely by tilt, the effect of distance of distance to the sun is only around 1%.
As for why the northern winters are colder than the southern, I don't think they are. Afaik, they're 1% milder than they would otherwise be due to earth being near aphelion. Is there a link around to a reference for this? It's not a familiar claim to me.