I just edited my post... looks like I was tired or confused when I wrote it.

The Weber DCOE's are not standard on the Murena, and have plenty of adjustment capabilities - it could be correct, but it sounds like it's slightly incorrect.
Even though it's expensive, the best thing would be to have a carburettor specialist check them on a rolling road.
On the other hand, if this is only occurring when you are running on the choke, I wouldn't worry too much. The thing is that when the choke is closed and you open the throttle wide with engine running relatively high RPM, you will end up with a very rich mixture - and this may limit performance greatly.
On the other hand, if you feel it is wrong, it may well be, and my own experience with my single Solex 34CIC (on a Holbay cam) is that cold starting has improved significantly after I have renewed gaskets and seals in it.
Do you know who did the Weber conversion?
- Anders