Summing multiple sheet range based on column and offset row lookup

My spreadsheet has a sheet for each month. Each sheet has a row for each employee in that month as well as a column for each active project in that month. I would like a summary sheet that: (1) sums the hours for each person per project for the entire year, (2) if possible, maintains the list of employees so they don't have to be copied to the Summary sheet, and (3) if possible, maintains a list of projects so they don't have to be copied to the Summary sheet.

To make things difficult: Hours are reported by week, so there are multiple lines per person. Not every person exists on every sheet. Not every project exists on every sheet.

The Summary sheet in the attached example contains hand-calculated values.