Reynard, reading your campaign idea sounds like you are aiming for an old-school style wilderness based sandbox with challenging site-based dungeons out in the wilds. Love it. Plus you want to make sure the players need to do some planning and resource management. Here are some thoughts:
Encumbrance
Use encumbrance. A strength 10 character can carry 150lbs all day, no problem, according to the core rules. That's patently ridiculous (I'm sure lots of folks here are veterans and hauled heavy rucksacks all day - these are extremely fit people and they didn't haul 150lbs). Using encumbrance (PHB p176) that 10 str character is now limited to less than 50lbs. Water and rations are heavy, as well as armor and weapons. Trust me, the carrying capacity will go fast, tough choices will be need to be made, and they'll be looking for pack animals or hirelings and dealing with real logistics.
XP for Gold
I believe this is the biggest change to drive an exploration game (unfortunately it's a big change). Return to a pre-WOTC approach like XP for Gold and little or no XP for fighting. The math is simple to implement, but you need to alter your campaign so there are meaningful uses for money along the way. I prefer allowing building of structures and castles like in older editions and encouraging a settle-the-wilds domain game in downtime.
Part of the reason wilderness fights are unsatisfying is characters go super-nova, they get regular experience for winning an easy encounter, and it's a 5-minute workday (sometimes two fights in a day if random encounter rolls were unkind). Thus many referees want to change the rest system and the healing system so characters don't recover daily in the wilds. Shifting to alternate XP makes wilderness combat a time-waster and distraction from the real goals of exploring dungeons and finding treasure - in other words, return random encounters to acting more like obstacles to be avoided through smart play instead of cakewalk XP.
Leave Utility Magic Alone
I'm of the opinion that you leave utility magic alone and don't overhaul the magic system. If a Druid wants to use their level 1 spells on Goodberry to make up for lack of rations, that's a valid choice and they're hurting their combat abilities to do it. Ditto with Create Water for Clerics. "You're going to wish that was healing word when you're in the dungeon..."
Furthermore, if you go with XP for Gold, there will be plenty of trouble dealing with encumbrance issues for coins, crystals, jewelry, fine statues, and whatever other oddball (and heavy) treasure they recover.
Healing and Gritty Realism
Changing the rest cycle from daily long rest to weekly (or longer durations) has downstream effects on the whole system. One house rule I've heard is simple - just add a level of exhaustion to any character that goes to zero hit points. 5E combat can be a bit like an elevator (up and down, up and down) and this rule may be too punishing, but I intend to try it out and seems to scratch that 'combat damage should be a scary' itch while leaving other systems intact. Each long rest only heals a level of exhaustion so a brutal fight could force several days of rest on a party, which seems to be what you are after (at least until the clerics are high enough to burn lots of lesser restorations).
I used most of these suggestions in my current
Tomb of Annihilation campaign, and it's really felt more like 70's D&D (albeit with gonzo over-powered player characters, but the players love it). As the characters level up and the focus of the game changes, it's okay if some of the resource management from lower levels gets easier through magic- it actually feels like an accomplishment after slogging around with rations and worrying about encumbrance.
I'm an old school blogger in the process of making peace with 5E - I posted some of these thoughts a few months ago:
Can 5E Play Like an Old School Game
Make Treasure Great Again