IMHO, come for a week or two in a vacation ( like Easter) and have a ton of resumes and get them out.
The area is very hospitable ( I came from LI over 40 years ago and never left; married a local boy, had kids, raised them here and had my career here and never will regret a minute. We are now retired here and not snowbirds
)
Accounting and business do go with the banking climate here. Come, see, try it out and remember, if you desperately need a dose of "big city", Toronto is closer than NY (2 hour drive). I love small town/rural (I live backed up to a hayfield 20 miles from the city, it was a 30-40 min. commute to work) It is slow-paced here in relation to Albany and certainly to LI.... so I suggest coming, looking for a job and checking out the area.