OK, you were right: No need to fool around with insolation sensors when a picture will tell you more. In my case it told me that solar may not be a good choice.
It was sunny today, and since the winter solstice is only 2-3 weeks away, I'd get a good idea of the situation today. So around solar noon (about 11:30 local time) I crawled up the ladder and saw that the whole roof is in the shade of the leafless trees
Looking North:
Just to get an idea of how deep into the shade it is, I took a shot from the north corner into the sun:
You can see that the sun is not even near the tips of the branches. To the west is a window which would give at most ~1 hour of direct sunlight before the sun hides behind the pine trees. In the summer I might get good solar, but I doubt that the amount of energy coming through between the tree branches would help our heating system in the winter. And next year those trees aren't going to be any shorter