Sure, here is a test case generator for the "Monday-Saturday Prime Factors" problem:

```python
import random

def is_monday_saturday_number(n):
    return n % 7 == 1 or n % 7 == 6

def generate_monday_saturday_numbers(limit):
    monday_saturday_numbers = []
    for i in range(2, limit):
        if is_monday_saturday_number(i):
            monday_saturday_numbers.append(i)
    return monday_saturday_numbers

def generate_test_case():
    limit = 300000
    monday_saturday_numbers = generate_monday_saturday_numbers(limit)
    
    test_cases = []
    number_of_cases = random.randint(1, 10)
    for _ in range(number_of_cases):
        test_case = random.choice(monday_saturday_numbers)
        test_cases.append(test_case)
    
    test_cases.append(1)  # End of input
    return test_cases

# Example of generating a test case
test_cases = generate_test_case()
for tc in test_cases:
    print(tc)
```

This script defines several functions:
1. `is_monday_saturday_number` checks if a number is a "Monday-Saturday number".
2. `generate_monday_saturday_numbers` generates all "Monday-Saturday numbers" up to a given limit.
3. `generate_test_case` generates a random list of "Monday-Saturday numbers" and appends a `1` to signify the end of input as per the problem statement.

The generated test cases will be random but constrained within the problem's limits. The script makes sure the "Monday-Saturday numbers" are chosen correctly and the input format follows the given constraints.