Ginore,
No, there is clearly not a registry for engine numbers from our Pagodas (or other contemporary MB cars).
Hard to find out from when exactly your particular engine was.
A small hint:
a) look up in the Engelen book (our Pagoda bible)
b) 23885 280 SLs were built (the only MB cars with the 130.983 engine). Among these two thirds were cars with automatic transmission (with a -12- or -22- in their corresponding engine number and the other third being stick shifts (with a -10- or - 20- in the center of their engine number).
Now,
all manual engines or automatic engines were numbered separately. That counts up to roughly 16,000 auto engines (-12-, -22-) which were built and about 8,000 engines for stick shift.
So, what's your serial number of the engine?
Roughly calculated, if your auto engine (130.983-12-0xxxxx) had a serial no. of about 6000-7000, the correponding car's serial were roughly about 010000.
This is only a very rough match, a closer one could only be obtained with the help of the databases of changes in the "Engelen" or - if you had the data card of the car where the engine was taken off (which in utmost cases you naturally do not have).
As to the exhaust, don't worry.
All 280 engines (all 250 engines and the late 230 engines) had or have the short casted exhaust headers and the exhaust down the headers is exactly identical on all these later Pagodas.
So, go out hunting for a new exhaust system!
Good luck!
Achim
(early exhaust headers)