Jark: Welcome to Rochester. You have actually found why Monroe County is one of the top counties to get a permit in. The wait time can vary from 4 months to almost a year, depending on the volume at the time you submit the paperwork. You actually helped by sending all the info ahead of your move. The clerks' office has become more and more agreeable in regards to permits. Both the county clerk and the county exec are firearm friendly.
On another note, now you can get some training and have fun too! Stop out to a range called the Genesee Conservation League, which is just East of Rochester in Penfield. Every Tuesday I run a concealed carry shoot that draws one of the best crowds of shooters in the area. The match is built around a scenario and we emphasize good tactics and safety, which we will teach you. We start at 5:15 and run until 9. There is a new shooter orientation to get you geared for the scenarios and then, for your first night, you shoot for free! PM me for directions or more details.