Another approach might be with a pivot table. These are great for such tasks. It could replace the monthly totals table. Maybe better on a separate sheet.
Or, you could leave your current table and use GETPIVOTDATA formulae to extract the results from a pivot table. So the pivot table might be on another worksheet and your current summary links to it.
Another good approach would be to use SUMIF formulae and define the correct range by using a combination of OFFSET, INDEX & COUNT. For example for month K3 = October, use INDEX to find the first instance of October in column A and COUNT to know how many. Then OFFSET from A3 to define the particular range. Be careful with this approach to make sure the year is the correct one if the data extends across more than one year.
Or, less simply, you could use a query table with a TRANSFORM crosstab summation.
I guess there are many ways.
HTH
Fazza