I do not know how it is in the US, but in Europe, each car has its circulating permit. In it you should find how many CC's the engine has and other info, that is, if such document exists!
The S-type Jag had twin SU HD6 1 3/4 inch carbs, whereas the 340/380/Mark II 3.4/3.8 had twin SU HD6 1 3/4 inch carbs.
Your engine number being 7B 6033-9 should imply its a 3.4 S-type engine. 3.8 S-type engines, (engines in the 380 where considered such) have a 5 figure number startin 50001 and up, following the prefix 7B. the last suffix,7, 8 or 9 indicates the compression ratio.
The other number you posted is a chasis number. P1R6472DN. P indicates the car was fitted with power steering, and DN means the car was fitted with overdrive. As for the R, I am not aware of the existance of such suffix. Could it be a B instead?
How is the car badged? 380 were badged 340 and below 3.8
danny