To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables for the quantities of kayaks and canoes to be made, formulating the objective function that represents the total profit, and establishing constraints based on the available assembly and quality checking times.

Let's define:
- \(x_1\) as the number of kayaks to be made,
- \(x_2\) as the number of canoes to be made.

The profit per kayak is $300, and the profit per canoe is $450. Thus, the objective function to maximize profit (\(P\)) can be written as:
\[ P = 300x_1 + 450x_2 \]

Given constraints are:
1. Assembly time: Each kayak takes 60 minutes of assembly, and each canoe takes 80 minutes. The total available assembly time is 8000 minutes.
   - \(60x_1 + 80x_2 \leq 8000\)
2. Quality checking time: Each kayak requires 15 minutes of quality checking, and each canoe requires 25 minutes. The total available quality checking time is 4000 minutes.
   - \(15x_1 + 25x_2 \leq 4000\)

Non-negativity constraints (since the number of kayaks and canoes cannot be negative):
- \(x_1 \geq 0\)
- \(x_2 \geq 0\)

Symbolic representation in JSON format:
```json
{
    'sym_variables': [('x1', 'number of kayaks'), ('x2', 'number of canoes')],
    'objective_function': '300*x1 + 450*x2',
    'constraints': ['60*x1 + 80*x2 <= 8000', '15*x1 + 25*x2 <= 4000', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

# Create a new model
m = Model("Kayak_Canoe_Optimization")

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.INTEGER, name="kayaks")
x2 = m.addVar(lb=0, vtype=GRB.INTEGER, name="canoes")

# Set the objective function
m.setObjective(300*x1 + 450*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(60*x1 + 80*x2 <= 8000, "assembly_time")
m.addConstr(15*x1 + 25*x2 <= 4000, "quality_checking_time")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of kayaks: {x1.x}")
    print(f"Number of canoes: {x2.x}")
    print(f"Total profit: ${300*x1.x + 450*x2.x:.2f}")
else:
    print("No optimal solution found")
```