Example 7 Fill a 9-row, 1000-column table (one number per cell) with 9 ones, 9 twos, 9 threes, ..., and 9 thousands, totaling 9000 numbers, such that the absolute difference between any two numbers in the same column does not exceed 3. Let the minimum value of the sum of the numbers in each column (a total of 1000 column sums) be $M$. Find the maximum value of $M$.
We solve for the minimum value of the column sum $M$ based on the different scenarios of the number of columns in which 9 ones are distributed.
If the 9 ones are distributed in the same column, then $M=9$.
If the 9 ones are distributed in two columns, then the sum of these two columns is no less than $2M$, and by the given condition, the maximum number in these two columns can only be 4, so the sum of these two columns $\leqslant 9 \times 1 + 9 \times 4 = 45$, i.e., $2M \leqslant 45$, so $M \leqslant 22$.

If the 9 ones are distributed in three columns, then similarly, we get $3M \leqslant 9 \times 1 + 9 \times 4 + 9 \times 3 = 72$, so $M \leqslant 24$.

If the 9 ones are distributed in four columns, then similarly, we get $4M \leqslant 9 \times 1 + 9 \times 4 + 9 \times 3 + 9 \times 2 = 90$, so $M \leqslant 22$.

If the 9 ones are distributed in more than 4 columns, then in one of these columns, there must be a number greater than 4 (because the numbers 2, 3, and 4 total 27, which is not enough to fill all the columns where 1 appears), which contradicts the condition that the absolute difference between any two numbers in any column is no more than 3, so this scenario is impossible.
In summary, the minimum value of the column sum $M \leqslant 24$.
The following table shows that the minimum value of the column sum can reach 24.
\begin{tabular}{llllllllll}
1 & 1 & 1 & 2 & 2 & 6 & 7 & 8 & $\cdots$ & 1000 \\
1 & 1 & 1 & 2 & 2 & 6 & 7 & 8 & $\cdots$ & 1000 \\
1 & 1 & 1 & 2 & 2 & 6 & 7 & 8 & $\cdots$ & 1000 \\
3 & 3 & 3 & 2 & 2 & 6 & 7 & 8 & $\cdots$ & 1000 \\
3 & 3 & 3 & 2 & 5 & 6 & 7 & 8 & $\cdots$ & 1000 \\
3 & 3 & 3 & 5 & 5 & 6 & 7 & 8 & $\cdots$ & 1000 \\
4 & 4 & 4 & 5 & 5 & 6 & 7 & 8 & $\cdots$ & 1000 \\
4 & 4 & 4 & 5 & 5 & 6 & 7 & 8 & $\cdots$ & 1000 \\
4 & 4 & 4 & 5 & 5 & 6 & 7 & 8 & $\cdots$ & 1000
\end{tabular}

Therefore, the maximum value of the minimum column sum $M$ is 24.
(3) Comprehensive Estimation

Based on the conditions that the combination structure should satisfy, we conduct a comprehensive analysis as a whole to estimate the maximum (minimum) value sought.