If the goods are in the checked luggage, and the luggage is checked directly from Italy to the US (i.e. not taken into Germany), you should be able to get the VAT form stamped in Italy. The Germans are very good at that. In MUC Terminal 2, the customs office actually has its own luggage band for (already tagged) luggage with duty free goods, and they certainly will take luggage connecting within the EU, as long as the place where you get the stamp is the last place in the EU where you have access to the goods.

Now, I'm not sure of the layout at FCO, but if the goods can be ckecked-in (i.e. not fragile), I would try to get the customs stamp there. If problems take it in the hand-luggage.

In my experience, the Tegel customs office might be slow, and they are very strict with the rules. If your home address is missing on the form, you will not be able to write it later, as it should be written in at the shop!