2.4s fit 147s no problem - the 147/156/GT are different versions of the same car and they didnt "weld in a 156 front end" to the 147GTA to make the V6 fit, the engine bays of 147s, 156s and GTs are the same size.
The problem would be finding a body computer that would allow a 2.4 in a 147, but there must be a way round it as Alfa raced some 147 2.4s a few years back.
It wouldnt "handle like a pig" at all - 156 GTAs with the 3.2 Busso are heavier than 156 2.4s, it would handle similar to a 147 GTA.
Been talked about before many times and would be a great conversion to do, especially if it was a tuned 20V - youre looking at almost 300bhp/450lbs/ft, those 5 cylinders sound great.
A highly tuned 1.9 like Zbrsk's would prob offer 98% of the performance for lighter weight tho . . . just wouldnt sound as good or be as special.