To solve this problem, we'll create a Gurobi model that incorporates all the given constraints and objectives. The goal is to minimize or maximize certain variables while adhering to the constraints provided.

Given the complexity of the problem with numerous constraints on sourness index, healthiness rating, and iron content, along with the ability to use fractional amounts of some ingredients, we will focus on setting up the model correctly.

We'll define variables for each ingredient (black beans, tomatoes, lemons, sashimi, apples, cherry pies) and then apply all constraints as given. Note that without specific coefficients for sourness index, healthiness rating, or iron content for each item, we cannot directly write the objective function or all constraints. However, I'll outline how one would approach this with Gurobi in Python.

```python
from gurobipy import *

# Create a model
m = Model("Food_Optimization")

# Define variables (assuming all are non-negative)
black_beans = m.addVar(lb=0, name="black_beans")
tomatoes = m.addVar(vtype=GRB.INTEGER, lb=0, name="tomatoes")  # Integer constraint for tomatoes
lemons = m.addVar(lb=0, name="lemons")
sashimi = m.addVar(lb=0, name="sashimi")
apples = m.addVar(lb=0, name="apples")
cherry_pies = m.addVar(lb=0, name="cherry_pies")

# Add constraints
# Sourness index constraints (example, actual values needed)
m.addConstr(black_beans + sashimi <= 138, "sourness_black_sashimi")
m.addConstr(lemons + apples <= 190, "sourness_lemon_apple")
# ... add all other sourness and healthiness constraints

# Healthiness rating constraints (example)
m.addConstr(tomatoes + sashimi <= 68, "health_tomato_sashimi")
# ... add all other healthiness constraints

# Iron content constraints
m.addConstr(black_beans + lemons <= 317, "iron_black_lemon")  # Assuming black beans and lemons have an iron contribution of 1:1 for simplicity
# ... add all other iron constraints with correct coefficients

# Other constraints
m.addConstr(-sashimi + 6*apples >= 0, "other_constraint_1")
m.addConstr(tomatoes - 6*cherry_pies >= 0, "other_constraint_2")
m.addConstr(black_beans + 3*tomatoes - 9*lemons >= 0, "other_constraint_3")

# Objective function (example: maximize healthiness rating)
# This would typically be based on specific coefficients for each food item's healthiness
m.setObjective(tomatoes + sashimi, GRB.MAXIMIZE)

m.optimize()

for v in m.getVars():
    print(f"{v.varName}: {v.x}")

print("Obj:", m.objVal)
```

Note: The above code is a simplified example and actual implementation requires precise coefficients for sourness index, healthiness rating, and iron content for each food item. Additionally, the objective function needs to be clearly defined based on the problem's requirements (maximize healthiness, minimize iron intake, etc.).