Seems like basically a bit more complicated version of a 4e SC with the goal being "complete the journey in good shape." What I like about the SC system is that it fits almost anywhere, you don't need a whole other different system for "social situation" or whatever (admittedly combat is its own thing).I guess to bring this back to the OP, the TOR system could be converted to focus on rewards rather than just draining resources, as well as rewarding preparation by having resources give advantage and lacking them giving disadvantage on hazard checks and preliminary rolls.
The other thing I'd say is that if you want travel to be engaging and challenging, don't let the party get a full rest during a journey unless they get a reward or have a stopover in a safe place that would make a full rest make sense. Like let them spend hit dice, maybe devise a table or something for regaining some resources spent during the journey when they succeed on hazard checks or have a leg of the journey without any hazards, but they end the rest with resources spent. They end the journey with that level 1 slot for goodberry spent, and the level 2 slot for pass without trace they used to get +10 on the check to bypass the bandit camp, and the hit dice they lost due to a failed hazard check to ford the icy river, etc, all spent.
When tou combine dynamic costs with reward focused challenges, you encourage exploration because if they don't explore they can't ever get those sweet rewards that might negate whatever price they've so far paid. They might find the Great Fairy's Fountain and spend the night there, taking a full long rest and gaining water skins full of fountain water that gives them all the water and calories they need for the day on top of 2d10 thp that lasts until the next dawn, from a single sip. Or they might just find a cache of gems and a spellbook, magically preserved from a time so long past that they've no reason to thnk anyone still owns it. Or they might see something so magnificent that they all gain Inspiration. But not if they don't explore.