Alright, short rest. After messing about a bit longer, here's an idea that might work for the videogame: Have it just be automatic after every normal combat encounter. Just give it to them.
Hear me out now; This ISN'T without a drawback..
I feel like camp spamming right now is too powerful/trivializing and I hope (Though some may HATE this idea, us Wizards ESPECIALLY) that you eventually have a hard number of these long rests you can spend on each segment of the game. I'd rather them be done automatically at certain thresholds and it is shared up front when and where they might be.
(Such as the Tiefling's camp intersecting with yours for the party if you rescue them)
If soft locking is a concern, keep the food as is and HEAVILY reconsider enemy strength compared to the PHB and Monster Manual. Right now you pretty much HAVE to long rest between most encounters involving 3 or more enemies and the action economy isn't already in your favor because of how 5e treats combat momentum.
Otherwise you might as well just implement a DOS2 bedroll and insta long rest and be done with it.