I recently had the original exhaust removed (and subsequently replaced) by the dealer on my wife's 2.5 N/A..and it's 2.5", as is the manifold downpipe flange, all of which supports the service manual data. Though it is indeed an S-Type with slightly higher output. I can only therefore reiterate my original comments, according to the service manual and related data only the 2.0L motor had this small pipework. Which may explain your comment as to the 2.5 N/A having no power to start with..it certainly wouldn't with that exhaust IMHO.
I was also recently supplied with a complete cat back Blitz system by Abbey, who absolutely guaranteed it was correct for the N/A or the turbo motor..it was a little over 76mm. (3") The primary difference twixt the RB25DE and the RB25DET is apparently in the manifold and downpipe. Addendum, the Blitz did in my opinion play havoc with the power band and delivery on the 2.5 N/A, though I did have a decat inline as well. I concluded it may be OK with the cat in place, but more power was released by losing the cat than by adding the exhaust on the N/a motor.
Managed to find one from an RB25DE now - cheers tho!I think the RB20 downpipes are 2" aren't they? The RB25DE is 2.5" ??? If you can wait about 5/6 weeks you can probably have mine as I'm engine swapping to an RB26 - couldn't tell you the condition it is in until we've taken it off though.
EDIT - Found this: