Cheese as a Food Group that can Help
(TL;DR You don't need to roll every day if the party uses this approach, but on the real tough days (DC's > 15), there will be some rolls that reflect how Out of the Abyss is a hard adventure).
Get Help when Foraging
This approach may smell of rules manipulation, and will only work if you accept this as the DM. The party and NPC's together can create advantage on all of the foraging efforts by using the Help rules for ability checks. As you do not define a DC I'll offer three examples when I sum up.
Rule of Thumb: Advantage amounts to a +5 on a given ability check.
As the DM, you first need to determine the following: since it's a survival situation, is there a valid reason that the NPC's will not help foraging? It's their necks too if they all starve. If there is a reason that the NPC's can't or won't forage, then what follows is at best partly applicable, and possibly inapplicable.
Working Together
Sometimes two or more characters team up to attempt a task. The
character who’s leading the effort—or the one with the highest
ability modifier—can make an ability check with advantage, reflecting
the help provided by the other characters.
A character can only provide help if the task is one that he or she
could attempt alone. Moreover, a character can help only when two or
more individuals working together would actually be productive. (Basic Rules p. 59)
This works for foraging. Why?
- Searching for food is something you can do alone.
- Two people looking for fungus/fish/bugs/caviar/water have a better chance of at least one of them spotting food/potential food and water.
- Food and Water Requirements (Basic Rules p. 66)
A character needs one pound of food per day and can make food last
longer by subsisting on half rations. Eating half a pound of food in
a day counts as half a day without food. (Summary: after 3 (+ Constitution modifier) days without food (min of one) a character automatically suffers one level of exhaustion.
This matters because once a player character has exhaustion, that player gets disadvantage on further ability checks, which cancels out the advantage (+5) bonus of help. On the other hand, once enough characters have a level of exhaustion, help (advantage) can reduce the effect of disadvantage on skill checks (foraging/survival). In this regard, after some bad luck days or a few days of DC's at or near 20, not having disadvantage can mean the difference between success and starvation.
Exhaustion (p. 106 Basic Rules)
\begin{array}{r|ccc}
\text{Level} & \text{Effect}\\
\hline
\text{1} & \text{Disadvantage on ability checks} \\
\text{2} & \text{Speed halved} \\
\text{3} & \text{Disadvantage on attack rolls and saving throws} \\
\end{array} Once the foragers lose advantage due to exhaustion, the risk of a vicious circle of failed foraging looms. Foraging is a priority concern for this phase of the adventure.
As in RL, water is the more critical resource to avoid exhaustion. The gathering rate for a successful foraging check (water) is 1d6 + wisdom gallons. (DMG p. 111).
Water Requirement: One gallon of water per day (Underdark, we'll assume that it isn't hot enough to trigger double requirement).
Half water rations forces a DC 15 Constitution saving throw of one level of exhaustion, added at the end of the day. Less than half rations automatically adds another level of exhaustion at the end of the day. If the character already has one or more levels of exhaustion, the character adds two levels of exhaustion. Lack of water triggers a compounding exhaustion problem, with the ability to forage impaired at only one level. Thirst kills.
Needed resources:
4 PC and 7 NPC ~ 11 gallons of water per day.
4 PC and 7 NPC ~ 11 pounds of food per day, with an occasional half rations day being acceptable.
Foraging rate: on a successful check 1d6 (+ wisdom bonus) pounds of food.
The objective: enough food and water to avoid exhaustion levels that harm the party.
Foraging and Difficulty
Top foragers:
Cleric has +2 Wisdom Bonus (per your data)
Rogue has a +1 Wisdom bonus (per your data)
Foraging check prospects DC 10:
With advantage (Help) cleric's the modifier amounts to +5. His +4
means even on a rolled 1, he finds food. Average of 5.5 pounds of
food per day. (1d6 + 2)
Rogue with a +3 and the +5 help has to roll a 1 to fail: 95% chance
to succeed with help. Yields an average of 4.5 pounds of food per
day.
- Warlock has a standard chance: +5 help means 80% Chance to provide
3.5 pounds of food.
- Paladin: +5 from help gets 80% chance of a successful forage for 3.5
pounds.
Average take: 5.5 + .95*4.5 + .8*3.5 + .8*3.5+ = 15.375 (15 3/8) pounds of food per day when using help. The prospects are very good, particularly if they over forage now and again to have enough for half rations for the day that everyone fails.
Bottom line: when the DC is 10, food isn't a problem if they use Help with foraging. They can store food for harder days.
Foraging Prospects for DC 15:
Cleric with Help is +9: a five or less fails. .75*5.5 average = 3.75
Rogue with Help is +8 so a six or less fails. .70*4.5 average = 3.15
Warlock with Help has +5 so a 9 or less fails. .55*3.5 average =
1.925
Paladin with Help has +5 so a 9 or less fails. .55*3.5 average =
1.925 lbs
At an average of 10.75 pounds per day, the party needs someone to go half rations most days, or get maybe the Dwarf Scout to forage as well with help.
Foraging Prospects for DC 20:
Cleric with Help is +9: a ten or less fails. .50*5.5 average = 2.75
Rogue with Help is +8: an 11 or less fails. .45*4.5 average = 2.025
Warlock with Help has +5: a 14 or less fails. .30*3.5 average =
1.05
Paladin with Help has +5: a 9 or less fails. .30*3.5 average =
1.05
At an average of 6.825 pounds per day, the party needs someone to go half rations most days, the Dwarf Scout ought to forage as well with Help (another 1.05 pounds from that pair), and maybe have another pair of NPC's do likewise. When the DC is 20, or high like that, getting that food is what makes possible getting the following day's food.
Resource issue: at the cost of a precious spell resource, the Cleric can create water (10 gallons, Create Water 1st level spell) if there is no water to be found. Because of how critical water is, see the compounding exhaustion point above, that may be a reason to save one spell slot on the really hard days to make sure nobody gets disadvantage the following day for the search.
The above shows how well they do when party members forage with an NPC performing the "help" function to assist with the ability check. While the Rogue and the Cleric are likely to get the most benefit since their Survival checks are highest, all of the character/NPC pairs can roll with advantage. This means that most of the time, they can forage enough unless you trigger conditions that prevent it. When DC's get very high, things get dicey, so that is when the rolls need to be made.
How does this answer your question?
Mostly, it means that if the party can concentrate on foraging and DC's stay 10-15, they can keep going. No need to roll (see the average foraging rates using Help) since they'll average enough food per day. That means that you only have them check when it is significant, or when a significant change of condition occurs:
- too much fighting to forage
- dead or incapacitated Rogue / Cleric who are the prime foragers
- Change in terrain/surroundings where the DC goes up
- NPC's die/leave and Help becomes scarce
- The DC established for a given day, or a given week, is higher.
You can control how successful the party members are in foraging by
adding or subtracting other encounters/things that occupy their
attention so that on some days, all of them can't forage.
Adjust the DC to any value you like, run the template again (when the terrain or conditions change significantly) and see how likely failure is. Then the fun part comes: the role playing interactions on who goes on half rations, who doesn't, and why? (Hint: keep the Cleric and Rogue fed! They are the party's seed corn). It's up to the party to play out the food distribution, with your input from the hungry NPC's.
Or, you can ignore all of that (if you feel that it's an exploit, and that this Underdark scenario in Out of the Abyss is trying to stress the characters in a survival situation) and not let Help operate in that manner. You're the DM, it's your ruling to make. What the above provides is a method within the rules that leaves you open to picking your spots where you make foraging matter and thus force a foraging roll since success or failure becomes significant on certain occasions.
FWIW, @BenBarden points out that if one gets down in the numbers, the +5 is a sweet spot for advantage rolls. If you go through the details at the link, you can see how the bonus for advantage will vary as the difficulty / DC / Target Number varies. You may want to adjust that "+5" - but the whole point of advantage and disadvantage a s a mechanic is to replace the fiddly bits of stacking plusses and minuses that we all know and love from previous editions. A good reason to consider just going with the +5 is on page 62 of the Basic Rules, the straight "+/5 for adv/disadv" is used for passive checks.
Best Answer
The rules as published work fine - there's no hard rule on determining which DC to use. That's why it's in the DMG, you're supposed to make a judgement call.
That said, the biggest issue with foraging in Chult is a potential lack of equipment to get potable water.
Of course, spells like Create or Destroy Water, Purify Food and Drink, and Create Food and Water can eliminate the issue entirely, but keeping them prepared and casting them daily are resources that could be otherwise allocated. (They're also only available to certain classes.) Other spells may help you make a fire to boil water, at least taking a bit of the edge off.
Tomb of Annihilation really hinges on the resource management part of old-school style gaming - Who's carrying how much of what? That said, between the set piece encounters and the random encounters, there are plenty of opportunities to separate the party from their survival gear.
...and that's when things get interesting. It's part of the challenge of the adventure. Trying to get around it isn't meant to be a matter of die rolls, it's meant to be an exercise for the players' minds.