I live in MN, in a house built in 1919, also with radiant heat. Foundation is concrete block rather than stone, but effectively the same for what we're talking about.
The ultimate issue with basement humidity isn't necessarily grading and moisture through the foundation (though that can contribute), it's the hot, moderately humid MN summer air cooling to basement temperatures, which increases the *relative* humidity of the air.
If you're sure that there's not much to be done from a grading issue* (no wet basement, no wall efflorescence), then the best approach is to run a dehumidifier. Depending on the strength of your dehumidifier and the size of your basement, running 24/7 may be a legitimate need.
If you're in the Twin Cities metro, I know that many library systems have electrical use meters available that you can use to see how much energy your dehumidifier is actually using. I replaced my unit last year, and I found that the electrical use dropped dramatically with the new unit while the humidity was managed much better. The difference in electrical use may not be entirely the dehumidifier.
Here's some anecdata from my extended family's homes in the MN/WI area:
-My house: built 1919, 1400 sq ft above ground, semi-finished basement, no central air, limited AC use upstairs, none in the basement. Dehumidifier is always plugged in and set for 60%. I keep my basement windows closed on the theory that it's easier to remove the humidity from a relatively static amount of air than from constant in-flows.
-House #2: built 1970, 2000 sq ft, finished basement, central air, basement humidity issues. Apparently, when this house was first purchased, the dehumidifier ran 24/7 and put out massive amounts of water. After a few years, it cut back to running only sporadically but the humidity was under control. Homeowner's theory is that the first few years of dehumidifier use "dried out" the foundation. I'm not sure I agree, because they also had the typical winter super-low humidity, so wouldn't that have continually "dried out" the foundation? They did some landscaping work including grade improvements for unrelated reasons, so my bet is that was the true cause.
-House #3: built 1990, 3000 sq ft, finished basement, central air, constant A/C use, no basement humidity issues. (Probably because the temperature and humidity differentials between the basement and upstairs are minimal.)
-House #4: built 1950, 2000 sq ft, unfinished basement, window A/C, basement humidity issues, Dehumidifier runs 24/7. Homeowners keep basement windows open.
-House #5: built 1920, 2000 sq ft, unfinished basement, window A/C, no basement humidity issues. (I cannot personally figure out how that works, but good for them.)
*Grade improvements don't have to be expensive. We've been dumping extra dirt, compost, mulch, whatever extra yard material we have in the berm areas on the side of the house with grade issues and over 2 years have built up a solid extra foot with minimal actual work and no extra cost.