Basement humidity in the NE is predominantly an air-infiltration problem, and dehumidification is usually only necessary in basements when the outdoor dew points are ~55F or higher (since 55F dew point air pulled into a 68F basement raises the relative humidity of the basement to ~65%.)
Here in the midwest the dew point is rarely that low in summer. Typical is about 65-68 F ambient dewpoint.
With high ceilings, multi-level and open stairwell from the basement it is tough to keep humidity in the basement in check. The neighboors all comment on having the same issues with temp stratification. Cool air sinks to the basement which is sitting on/surrounded by cool earth. In our case the delta from the upper floors to the basement runs about 8 F in summer. And that pushes 50% humidity air from the upper levels to around 60+% in the basement.
If I were to design the AC system for a home like this one from scratch (3 effective levels with open floor plan) I would set up the AC to work primarily as a dehumidifier in the basement...then recirculate/exchange air from there with other levels to do the temp control on those levels with only supplemental AC required for the other levels during peak demand (ambient north of 100 F).
If you air-seal the band joist & foundation sill with an inch or two of closed cell spray foam (or careful application of caulk & 1-part foam such as GreatStuff) and tighten up all exterior windows, doors & flues, the house pulls in less outdoor air into the basements and humidity loads for a whole basement are easily handled by a mid-sized room-dehumidifier. Many/most have provisions designed in for a hose attachment to allow draining to a sump or sink rather than relying on manual dumping. I have 1500' of basement, and a ~500W room dehumidifier that keeps the whole basement under 60% RH with PLENTY of margin, even with outdoor dew points well into the 70s. Mine is set up to drain into an existing sump.
Two things I would like to do eventually: tightening the walkout basement more, and adding a dehumidifier. The window installation in the walkout that the previous owner had done a few years ago was typical average tradesman level crappy work. Probably need to pull them out and reinstall to get it right because they have been a bitch to seal (rain blows through the casing at times.) What really irks me from the original house build is that there is no insulation at the header or band joists (builder was apparently allergic to insulation.) Nor is there any insulation in the plumbing/vent cavities in exterior walls that I've found so far. Putting it in after the fact is not so easy without remudding/resurfacing, and repainting all affected walls.
If you want to go one better (it's a bigger project, but with bigger payoff), insulating the basement walls to R15+ (1-2" of extruded polystyrene on the foundation walls + 2x4 studwall snugged up against it with UNFACED R13 batts, no interior vapor retarder/barrier of any type), the temp of the basement will come up several degrees, which lowers the relative humidity. (Depending on where you are in NY you may need more than 1" of XPS to prevent wintertime moisture accumulation in the studwall, but 2" would be more than enough everywhere.) If the basement walls are already finished sans-insulation, there may be other options, but the options depends on the particulars.
I did this in one of the rooms already that is north facing, used 2" XPS to fill each existing stud cavity snugly, not the batts as I feared moisture from infiltration. Made the room much more comfortable in deepest winter, as did adding an additional register so that it is now easy to set temps there, I can make it downright toasty now if I want just by manipulating the new register.
I need to insulate one other semi-full basement room this way (empty stud cavities behind painted/finished drywall at present...did I mention the builder's insulation allergy???), but am planning to convert it into a large 4th bedroom by cutting out a window for full egress, adding insulation/sound deadening to ceiling/living room floor, adding an air return and 2nd register, and enlarging a closet and adding a bedroom door (these latter two are tricky with the current stair arrangement.) I figure I can do the full project for a few grand and add about 15-20 k to resale while making the space much more usable/comfortable for guests and for the kids as a playroom.
The better mini-splits are WAY more efficient than window-shakers in cooling mode, and even at 20cent/kwh electricity cost less than half as much to operate than a state-of-the art oil or propane burner (about the same operating cost as $1.50/therm natural gas in a 90% AFUE burner when in heating mode when it's 20F outside, cheaper when it's 30F+.)
Our gas pricing has been about half that for the past three years. Electric here is less than you noted but keeps rising and is at about 14 cent/kwh. (With utilities cost it is always a matter of locale when trying to figure this stuff.) I considered a heat pump briefly for the whole house but it looked like a wash compared to nat. gas. I went with the nat. gas condensing at 95% AFUE. There were two major negatives to heat pump in my locale: 1. It rarely works well comfort-wise in existing homes (talking with other homeowners who had them, they warned me away) because of the lower delta T of the heated air relative to a furnace and the typical undersized ducts. On low temp days, 0...-5...-10...-15 F, strip heaters would eat our lunch cost-wise---we had some strip heaters in a home as a kid during a very cold winter and I remember electric bills that exceeded anything I've had in the 30 years since. We shut them off and used a pot belly stove and fan to heat ~2000 sq. feet after that. 2. A nat. gas furnace can be operated in a blizzard or ice storm when power is out for days as long as an aux. generator is available to run the blower/board circuit. (In the old days we used our wood fireplace and cooked using a wood cookstove along with kerosene lamps and were quite comfortable without a generator...milking the herd by hand twice a day was a pain though...) Perhaps the same could be accomplished using nat gas back up for a heat pump with the blower/board connected to aux. generator panel. I wasn't sure on this latter point.
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