AK and VT are not included in the numbers because you don't need any license in those states.
If NICS is down it could be a royal PIA if you have to return to the dealer (especially if you travel to an upstate dealer etc.). You can also get delayed for no reason. Some dealers will also give you a discount on transfers if they don't have to do a NICS check.
IF you have a NY license you are eligible to get a CT and NH CCW license. A NY license is good in ten states. They are: Idaho, Indiana, Kentucky, Michigan, Missouri, Montana, Oklahoma, South Dakota, Tennessee, Utah
If you don't have a NY license but you want a NH CCW license then you must get a FL CCW license first.
If you have a FL CCW license but no other license you can carry in 26 states. They are: Alabama, Arizona, Arkansas, Colorado, Florida, Delaware, Georgia, Idaho, Indiana, Kentucky, Louisiana, Mississippi, Missouri, Montana, New Mexico, North Carolina, North Dakota, Ohio, Oklahoma, Pennsylvania, South Dakota, Tennessee, Texas, Utah, Virginia, Wyoming
If you have a NY, FL, CT and NH license you can carry in 28 states in addition to NY.
Disclaimer: You should always check the latest information on packing.org for both accuracy and any state updates.