Create a numeric lookup field, use the month character as input and assign a numeric value to each month as output. Add both the character month and numeric month fields to the summary, hide the numeric month field, and sort it in descending order, then the character month field values will be in correct order.
Thank you, Mo! I also found another way to work around my issue by setting the 'Matching' setting to 'Values from table' then ordering the months the way they should be in that table and applying it on the 'Sorting' tab. I will keep your suggestion for future summary building as it seems efficient as well.