The harps I have listed as 'Italian baroque' (NMM through to Bologna 3) date from between about 1600 to 1750. There is at least one later Italian baroque harp that I am aware of, the triple harp by Vetorazzo, made 1793, now in Leipzig (Rimmer 1966). However the Italian baroque harp largely died out with the invention of the pedal harp in the later 18th century.
It is my supposition that the Italian baroque form developed in at the end of the 16th century, from a fusion of Spanish and Gothic features. The main characteristics of Italian baroque harps is the raised bass end of the neck, and the use of scrolls instead of peaks to decorate the neck. The soundbox is tapered and is usually wider and deeper than gothic harp soundboxes, but not as wide and deep as Spanish harp soundboxes.
Many Italian baroque harps have two or three parallel rows of strings to provide chromatic notes, but some were diatonic.
The name of this instrument in Italian seems to have been 'Arpa Doppia' which does not refer to the multiple ranks of strings, but to the large size and bass range and power of the instrument, like a 'double bass' or 'double bassoon'. Italian baroque harps seem to have been played in France and England as well as in Italy.
There are surely more Italian baroque harps extant than I have listed here. I will be grateful for details of any that you can provide.