I have the same car and symptoms as you.
Plus: during the first few kilometers (miles in your case :-), the engine stumbles heavily if demanded in high gears. If you reduce to a lower gear you can accelerate and after that the problem tends to disappear, but still dead engine below 2700rpm or so.
I connected Fiat MultiEcuScan and logged "desired turbo boost" vs "boost pressure", accelerating in a single gear from >1Krpm to around 4500rpm. The measured boost value was clearly below the required value, slowly approaching above 2500rpm or so (but still below the desired value). This doesn't happen in my 159 with almost the same 1.9 16v JTDm engine: from 1900rpm or so the desired and actual values are quite close to each other. So I have a boost problem in the 147: either bad turbo, or stuck vanes or vacuum pipes / control valve.
Will give the MAF a good clean, too. Let's see what happens. Please let's keep each other updated.