Painted Dash 912's were built from April '65 in BOTH the Porsche & Karmann factories simultaneously.
35xxxx - Porsche Factory
45xxxx - Karmann Factory
Due to the Karmann factory having more resources (man power & equipment/size), they completed approx 1500 painted dash cars, whilst Porsche completed approx 750 (not confirmed exact numbers). High numbers of US ordered vehicles forced the 'out-sourcing' , but quality was maintained.
The one you inspected (350557) would imply the 557th built at the Porsche factory (who predominantly built for the European & Australian market etc), which would confirm the '65 build. COA would confirm the date of completion along with engine/gearbox numbers along with paint codes and options (to see if the gauges / sway are OG?).
It is likely at some stage someone has painted the dash and installed trim to 'update' the look of the dash to a 911 (912's after the painted dash era were adorned with brushed Alluminium dash trim).
You have my details if you'd like any other info, and the guys on this forum like Chris, Lee, Steve and others are very knowledgable and can also help.