To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables and translating the objective function and constraints into algebraic terms.

Let's denote:
- $x_1$ as 'hours worked by Jean',
- $x_2$ as 'hours worked by George'.

The objective function is to maximize: 
\[8.61x_1^2 + 8.54x_1x_2 + 1.04x_2^2 + 3.32x_1 + 8.36x_2\]

Given constraints:
1. Jean's work quality rating is 17, which translates to $x_1 = 17$ if we interpret "work quality rating" directly as hours worked, but this seems more like a characteristic of Jean rather than a constraint on hours worked. Thus, it might be better represented in the context of the problem as an attribute or factor influencing other constraints rather than a direct constraint.
2. George has a work quality rating of 6, similarly translated as $x_2 = 6$ under the same interpretation, but again, this seems more like an attribute.
3. The total combined work quality rating from hours worked by Jean squared and hours worked by George squared has to be 49 at a minimum: $x_1^2 + x_2^2 \geq 49$.
4. $3x_1^2 - 9x_2^2 \geq 0$.
5. The total combined work quality rating from hours worked by Jean plus hours worked by George should be 152 or less: $17x_1 + 6x_2 \leq 152$ (assuming the "work quality rating" is used here as a multiplier, which might not directly translate from the given attributes).
6. The total combined work quality rating from hours worked by Jean and hours worked by George must be 152 at maximum: This seems to repeat constraint 5, so we'll consider it as $17x_1 + 6x_2 \leq 152$.
7. Hours worked by Jean must be an integer.
8. Hours worked by George must be an integer.

The symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x1', 'hours worked by Jean'), ('x2', 'hours worked by George')],
    'objective_function': '8.61*x1**2 + 8.54*x1*x2 + 1.04*x2**2 + 3.32*x1 + 8.36*x2',
    'constraints': [
        'x1**2 + x2**2 >= 49',
        '3*x1**2 - 9*x2**2 >= 0',
        '17*x1 + 6*x2 <= 152',
        'x1 == int(x1)',  # Symbolic way to represent integer constraint, actual implementation will vary
        'x2 == int(x2)'   # Same as above
    ]
}
```

Now, let's implement this in Gurobi Python:

```python
from gurobipy import *

# Create a new model
m = Model("Work Hours Optimization")

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_jean")
x2 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_george")

# Set objective function
m.setObjective(8.61*x1**2 + 8.54*x1*x2 + 1.04*x2**2 + 3.32*x1 + 8.36*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1**2 + x2**2 >= 49, "minimum_work_quality")
m.addConstr(3*x1**2 - 9*x2**2 >= 0, "work_balance")
m.addConstr(17*x1 + 6*x2 <= 152, "maximum_total_rating")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Jean: {x1.x}")
    print(f"Hours worked by George: {x2.x}")
else:
    print("No optimal solution found")
```