Teddy Bear you are right, you can run your Southern Pride on number ten wire at 240 volts and even a 300 series Cookshack. Wire size is determined by amps rather than voltage, it must have relate to resistance to current flow rather than voltage.
Therein lies the limitation of Honda generators of this size. Even if they are the coolest thing since pulled pork. Brand X or even a bigger Honda with a 240 hook up will give you up to 30 amps of 240 volt power on one number 10 wire cord which is 6000 watts total.
I have a small electric sawmill that requires 40 amps of 240 to start, but runs at about 28 amps. Getting the cords and the connectors all figured out was quite expensive so that you could break it down for transport. Even so I try to keep the total cord lengths under 50 feet.
PS: Konrad, I checked out the Kubota diesel sets online and they look really nice, pricey but like a good fit if you are going to be running almost exclusively on your own power. Do you know any place in this area that has them in stock, like a tractor dealer?