I agree with Sybille: the American Italian hand seems to be quite distinct and is probably best regarded as a nineteenth century confection. Time for a digression, methinks ...
Those bulbous ascenders which got on Alfred Fairbank's nerves seem to have originated in Italy in the late 16th century but quickly became a feature of English writing. They were probably rather old fashioned in Bickham's day, by which time the English round hand had evolved as a distinctive style in its own right. It seems that "Italian hand" was defined as narrower and lighter, and considered suitable for ladies, whereas the new round hand was a business script above all.
Just for once I find myself in agreement with Fairbank. It all started off well as a mild modification of cancellaresca involving a turning of the pen, but the big bulbs used by the likes of Edward Cocker in the late 17th century look contrived and rather tasteless. Fairbank blames the engravers for everything he dislikes (all writing between Bartholomew Dodington and Edward Johnston, in effect) and he may well have a point, but I reckon you also have to suspect poor taste and showmanship on the part of the writing masters.
Incidentally, the wedged shades on Spencerian "t", "d" and "p" are perhaps descendants of those Italian hand bulbs. They're also susceptible to over-emphasis and best kept relatively modest in my opinion.