Are you sure you overwrote all of the necessary files? Specifically the files affected by CORE-1349 are in /components/invoice_templates/. What would happen before CORE-1349 was that PDF invoices would send headers and output the PDF document, but execution would continue. This would result in additional headers being sent which produced an error of "cannot send headers, headers already sent".
As of CORE-1349, all invoice templates shipped with Blesta (default and quickbooks) now terminate execution immediately after the PDF is output, which completely prevents additional headers from being attempted. Moreover, no headers are sent prior to PDF output, so if CORE-1349 doesn't resolve the issue for you, the issue must be with either custom changes, or outside the control of Blesta (e.g. server related).