Just a couple of points ...
(1) Will your consulate/embassy issue you an "Emergency Travel Document" (or the equivalent), as the passport reissue will take so long?
(2) Do you have a driver's licence, or some other form of "Government-Issued Photo-ID?" For flights within the Schengen zone, any such approved document will suffice for check-in and boarding flights.
(However, I know neither your nationality nor your home-base location, so the above points may not even be relevant!)
-- Henry