Thanks everyone.
The kWh cost is low (actually only about 60% of the bill I'm looking at), the rest is fuel surcharges and taxes, so I'm fairly confident in my assessment of the total running cost. A later test was showing closer to 300 kWh.
I don't have a furnace or a furnace fan; the house has radiant hot water heat. I did see something about a basement fan that vents outside? Not sure what that would do, but seems like a relatively cheap solution if it'd work. I'm guessing that a whole-house dehumidifier system needs air vents, which I don't have.
I'm not really seeing much of an issue in terms of moisture impact, other than it "feels" humid down there. No rusting appliances or mildew. There is water after rain in one portion (a 1950s-era addition that wasn't as well done as the 1910s original), but we're working on addressing that by caulking stuff up inside and improving rain flow away from the house on the outside. I'd love to just leave it (in fact, that's what I'm doing now as I'm researching the issue), but I'm concerned that I might cause future issues. If I start getting mildew, can I just run the dehumidifier then to kill it? Or is it possible that if the high humidity is only seasonal (winters in Minnesota are SO DRY), that would inhibit longer-term moisture issues?
Rubybeth, your electrical costs seem pretty close to mine, though a little lower. I'm open to running the AC when it's cooler, but wouldn't that be a significant increase in the energy use, even compared to the crazy dehumidifier? Husband and children are home during the day, if that matters.
The basement is...partially finished? And I don't mean that part of it is finished and part of it isn't; I mean that someone framed out walls and ceilings (but not floors) across most of the basement at some point. The most recent prior owners tore out part of the drywall on one wall, but I don't know if that was for moisture issues or aesthetic effect.
Has anyone heard anything about calcium chloride (that is, road salt) dehumidifiers? It seems like an extremely mustachian solution (salt in a colander over a bucket, salt absorbs moisture, brine drips into bucket, evaporate the brine back to salt and repeat), but does it actually work? And how concerned should I be about small children getting into something like that? (They're not typically in the basement alone, though.)