I think my devices are messing with me. I used the test sketch above on the one that I have already wired and I got 80µA and 40µA for D2 and D3, respectively. I desoldered the wires and got 5µA in both cases. Maybe the other one is somehow damaged. But that’s not all. I soldered about 30cm of wire (open end, completely insulated, not touching anything) on D2 and that caused the current to increase to 18µA when D3 was in INPUT_PULLUP mode. The same thing happens with the wire on D3 and D2 in pullup mode, and soldering a wire to each increases the current even more. 
At least that is consistent with the higher readings when it was wired. But why? 