how were two-handed swords carried?

Probably over the shoulder like you would a polearm, sometimes in a scabbard, sometimes without. A more uncommon way would have been in a baldric over the shoulder (as seen in braveheart for example).

I've heard that back scabbards for such large swords is mostly a Hollywood invention and that seems right to me as the act of drawing a sword from your back seems clumsy and slow enough already, let alone drawing a Claymore or a Zweilhander.

Yes, it's almost impossible to draw it, if you carried it in a baldric you would unsling it long before any hostilities took place. The two handed sword isn't exactly a weapon you try to draw quickly in any scenario. IIRC Swiss pikemen and German Landesknecht soldiers are described as relying on daggers or short arming swords in close quarters (Schweizerdolch and Katzbalger respectively).

It seems that carrying a large bare sword without a sheath would expose the sword to the elements and leave its carrier open to accidents.

It's less or a problem than you think. So long as the blade is kept clean and oiled on at least a semi-regular basis the weather is not an issue and accidentally cutting yourself, well, it's harder than you think. If you try carrying a longsword around for a day you'll find that it's an unwieldly piece of equipment that weights 2-3 kilos, you tend not to wave it around much and generally put it down somewhere whenever you can. The only time you really draw it is when you expect to use it and when you do, you tend to know where the business end is.

Were scabbards that were slung around the back ever historically accurate for one-handed swords?

Yes but to my knowledge only short blades were carried that way and not commonly. I think the Japanese No-Dachi is carried across the back sometimes but I do not know enough about Japan to say for sure and it certainly isn't a short sword.

Did the method of carrying two-handed swords differ across countries in medieval Europe?

Not really. You carry it in your belt on the opposite side of your sword hand because that is the only way you can practically draw it.