Ah-ha! Well maybe not ah-ha but first I must ask your forgiveness for my repeatedly getting on the Proof Date bandwagon.
When you mentioned the letters you didn't say they were cursive. The Proof Date letters are of course in block form, not script.
I happen to own a NAVY ARMS .36 caliber Remington which also has cursive or script letters but the letters on it are (as near as I can figure out) G. U.
The G is quite stylized.
I am not saying that your gun isn't marked A.U. but is there is a chance that the first letter is a G?
Anyway, G or A, I recall reading somewhere that there were two different Uberti companies? I have looked thru my readily available modern Black Powder books and I can't find a good reference to the existance of two companies but as I say I seem to recall reading somewhere.....
Perhaps someone else on the forum can add to this thought?
Getting back to my Remington, it does have the proof date letters (XVI) indicating it was proofed in 1960 along with the other Italian Proof marks. It doesn't have a serial number unless the "18" marked on the bottom of the grip is one.
As I understand it, it is a law in Italy that ALL guns are proofed so I have no idea why your gun doesn't have those marks on it. Weird.
Good luck on your search and hopefully someone else will chime in on the script letters and how they tie the gun to a producer.