On a low mileage original car like that, there's probably nothing major wrong with the Pierburg. Whatever it is will probably be cheaper to fix that fitting a new Weber.
The problem is finding someone with the expertise who knows what their doing with the Pierburg thesedays, but they are out there - I can vouch for Northampton Motorsport in this respect:
www.northamptonmotorsport.com/
I'm up north, but it doesn't take that long to get there. The Pierburg is a superior carburettor to the Weber, but it more complex a beast, hence a lot of people don't have the expertise thesedays to fix them.
Is the car always revving at 1200 revs when warmed up? I can tell you that my Pierburg is 100% spot on, but in winter, when starting from cold, the revs do shoot up to 2k or so, then settle to about 1200 for a bit. Whilst this shouldn't ordinarily happen, the affect of cold temperatures on the bimetallic strip in the autochoke makes it contract more, hence resulting in more choke. In summer, this doesn't happen.