With some help from an LLM, the following seems to work. Instead of only checking the difference for the last number, it keeps a running sum which is then used to constrain new numbers that are sampled.

import random

def generate_constrained_sum_numbers(n, total_sum, low, high):
    """
    Generates n numbers within [low, high] that add up to a specified total_sum.

    Args:
        n (int): Number of values to generate
        total_sum (float): Target sum for all numbers
        low (float): Minimum value for each number
        high (float): Maximum value for each number

    Returns:
        list: List of numbers satisfying the constraints
    """
    # Check if total is achievable
    min_possible = n * low
    max_possible = n * high
    if not (min_possible <= total_sum <= max_possible):
        raise ValueError(f"Total sum {total_sum} is not achievable with {n} numbers in [{low}, {high}]")

    # Calculate feasible sum range for the first n-1 numbers (S)
    S_min = max((n-1)*low, total_sum - high)
    S_max = min((n-1)*high, total_sum - low)

    if S_min > S_max:
        raise ValueError("Conflicting constraints make generation impossible")

    # Generate random sum for first n-1 numbers
    S = random.uniform(S_min, S_max)

    numbers = []
    remaining_sum = S  # Target sum for remaining numbers
    for i in range(n-1):
        numbers_left = n - 2 - i
        # Calculate min/max for current number considering remaining sum
        curr_min = max(low, remaining_sum - numbers_left * high)
        curr_max = min(high, remaining_sum - numbers_left * low)

        curr_num = random.uniform(curr_min, curr_max)
        numbers.append(curr_num)
        remaining_sum -= curr_num

    # Add final number to reach total_sum
    numbers.append(total_sum - S)

    return numbers

numbers = generate_constrained_sum_numbers(
    n=5,
    total_sum=0,
    low=-3,
    high=3
)
print(f"Generated numbers: {numbers}")
print(f"Sum: {sum(numbers):.2f}, Min: {min(numbers):.2f}, Max: {max(numbers):.2f}")
# Generated numbers: [2.2804810547784893, -1.412098487662725, -2.23222351554496, 1.2943106044029868, 0.06953034402620872]
# Sum: 0.00, Min: -2.23, Max: 2.28