Sigh... How many times do I have to throw my money at you? Really, now.
This, line here, however, brings up a question based on this line here: You might lose hit points or spells or Supply during these challenges,
Can you tell us what you mean by the bolded bit?
I'm imagining that while a party can very easily RP the trip, including each encounter, it could also be handwaved away with die rolls for groups that (gasp!) don't care about such things ("The trip through the Dusty Desert takes three days. It's a difficult and trying time. You <rolls dice> gain two strife, one fatigue, and lose eight supplies").
But since spell slots and all hp are regained after a rest (in O5e, at least), then you won't lose such things for long, and the only time it would really matter--at least for parties that simply ignore the actual travel--would be on the last day of the journey ("You've reached your destination. <rolls dice> Bob, you're down three spell spots and 9 hit points.")
In the Let's Look At Exploration post, you said you can take long rests at campsites but can only lose strife and fatigue at havens. Are you changing how rests and regaining hp and slots work on capital-J Journeys?
Or do you mean spells and not spell slots? "Due to the desiccating winds of the Dusty Desert, you can't cast magic missile until you actively spend time preparing the spell again." I really doubt it's this one, although I can imagine a monster or weird magical encounter that could do such a thing.