This is the sort of game that I think Cortex would excel at. I could model multiple stress tracks: nutrition, health, injury, intra-party tension, finances. Every time the adventurers get a setback, they gain or step up a die in that stress. Max out a stress, and you get a serious crisis or fail-state. I'd put in a pool of expendable dice for supplies: food, medicine, pack animals. And I'd model the challenges like terrain, weather, disease, and relationships with locals as a pool to be whittled down.
The goal of the game should be something clear like, "Get from the Caribbean to the Pacific through the Darien Gap," or "Find the rumored ruins of Ixitxachitl, sketch them, and get out before the rainy season traps you." Play would focus on the party collaboratively filling in a map, with the GM throwing in curves and setbacks. If it's a campaign, each session could play through a particular sortie from base camp, from packing (committing expendable dice) through trekking (making the rolls) to consequences (suffering and buying off stress).
For an exploration-focused game like this, I'd want to lean heavily on player-generated input. What are the symptoms of this horrible new disease hitting the party? What do you have that the locals really want to trade for? What truths are you deducing about Ixitxachitl that the previous explorer got wrong? I'm used to providing this sort of content as a DM, but when discovery is the main reward, I've found the players' brainstorms are a big creative boost.