Sorry I can't suguest any engine / gearbox rebuilders but If I was having to resort to that kind of measure I would take my car to the garage that was the most familiar with it ie: a Fiat dealer or DTR (but if I remember correctly you have had problems with them).
As far as the stalling / stuttering problem goes. I had this with my car when I first bought it. first time cleaning the IAC valve seemed to sort it out.
After this I changed spark plugs twice in as many months! on the second time after removing the plug wire I looked closely in the plug recess to see water around the base of the plug.
After cleaning and drying everything out thoroughly (including cooking the coil packs in the oven at a very low heat) new plugs and then reassembled everything with a bead of silicone around the plug wire I have not had since (that was about 3 years ago).
Looking at the weather in the UK recently it may be worth pulling the plug leads off and looking inside for any moisture. costs nothing to check?!! also a new set of plugs are cheap.
Wife / Girlfriend may not be too happy about you cooking the car !
Good luck
