It used to be possible to directly query your experience progress with this command (you can replace smithing with any of these things):
In principle, you could save, do a bunch of smithing, check your skill advancement, load, deactivate the guardian stone, do the same amount of smithing as before, check your advancement again, and compare numbers.
As of patch 1.9, this no longer works, and a cursory examination of the available commands reveals no obvious alternatives. But if you still have an older version of Skyrim for some reason, this method ought to work for you. Otherwise, you'll have to eyeball it and/or smith enough to level up smithing. Instead of eyeballing, you might try taking screenshots of the Skills screen and overlaying them with your image editor of choice.
Having said all that, in my (limited) modding experience, the Active Effects page is rarely or never incorrect. If an effect does not get applied correctly, it's generally not visible in Active Effects, and I find that's the most reliable way of detecting these problems in the first place.