The Atlantic, The Pacific, etc
The Mediterranean, The Baltic, The Caspian
The Mississippi, The Amazon, The Nile
The Sahara, The Gobi
The Rockies, The Andes, The Himalayas
The South, The Mid-West, The Mid-East, The Rhineland
The Amazon (rainforest this time)
The Big Apple, The Windy City, The Outback
Those are still proper nouns, so yes it IS that hard.
"Going on a road trip from Chicago, driving through mid-west, and staying a night at Grand Canyon before backpacking in Mojave."
Can you honestly say that sentence is either proper or natural?
Yes, that sentence sounds proper to me. That's how I'd say it, at any rate.
Not that I really care anymore (c'est la vie), but I try to stay sharp on grammar because I have to write. So let's examine your examples, and going by my (sometimes imperfect) memory....
The Atlantic, The Pacific, etc: the modifies ocean, not the name, which specifies which ocean.
The Mediterranean, The Baltic, The Caspian: the modifies sea, not the name, which specifies which sea.
The Mississippi, The Amazon, The Nile: the modifies river, not the name, which specifies which river.
The Sahara, The Gobi: the modifies desert, not the name, which specifies which desert.
The Rockies, The Andes, The Himalayas: the modifies mountains, not the name, which specifies which mountain.
The South, The Mid-West, The Mid-East, The Rhineland: Those aren't even real names. They're just regional descriptions.
The Amazon (rainforest this time): the modifies rainforest, not the name, which specifies which rainforest.
The Big Apple, The Windy City, The Outback: Nicknames.