A very interesting topic, one that I've thought about quite a lot myself. I had always heard the style referred to as "fishbelly" until recent times, and have never quite adjusted to the term "perchbelly". Maybe the term is regional, I'm not sure.
Illinois is a melting pot of styles, since makers came here from all of the eastern and southern states, as well as most of the countries in Europe. There were a number of makers here who used the "fishbelly" architecture. While the majority of these makers did indeed come from New York state, there were also some who came from Ohio, Virginia, Germany, Ireland, and even Portugal. I would like to point out that not all fish/perchbelly stocks are the same. There are two distinct types. One type (type 1 for this discussion), is rounded from the trigger area clear back to the toe, truly resembling the belly of a fish. The other type (type 2 for this discussion) starts out like any other rifle with normal drop at the wrist, but makes an abrupt upward turn at the bottom of the wrist and is then quite straight all the way back to the toe. Type 1 has a comb with fairly normal drop, but the comb on type 2 forms a straight, or nearly straight, line with the barrel. I consider type 2 to be the more refined of the two, and it is seen on some very high quality rifles. The lines of type 2 can be fairly dramatic, with slender architecture and a long, pointed toe that is not unlike that on some southern mountain rifles. Anyone who questions the reason for the existence of fishbelly stocks in the first place, has never put one to their shoulder, or at least not one that fits them. These rifles hold very well, far better for me than any Roman-nosed rifle I've ever held.
As to the origin of the fishbelly/perchbelly style, it certainly seems to have originated in New York state, at least in this country. I have sometimes wondered whether the Dutch fowlers from a much earlier period in New York history, might have had some influence. They are among the earliest examples of this particular architecture.
There was an Illinois maker named Henry P Brunker, who came from upstate New York, and arrived in Ottawa, Lasalle County, Illinois, in 1848. He was without doubt our state's most prolific rifle maker, working from 1848 until 1871. I have seen over sixty of his rifles, of which just two were not type 2 fishbellies. I personally own 22 of them. Many are target rifles or "hunting & target rifles", and all are of first rate workmanship. The rifle on the cover (dust jacket) of my books is a Brunker, stamped BRUNKER & MITCHELL OTTAWA WARRANTED. It was made during one of Brunker's several partnerships and dates from 1856-1859.