I've finally implemented the feature I've dreaded for a year; it is now possible to interact with objects that are behind other objects.
I didn't want to disturb the possibility to hide casually behind other objects, so I made it work like this: If you move your player in behind an objects, so that it (your player) is obscured by that object, and stand still for half a second, all other objects that are wholly or partially obscured by the object obscuring your player will be drawn with yellow outlines, and at that point, you will also be able to click on them to interact with them normally.
I hope this fixes the problems with dropping bread behind ovens, buckets behind wells, and hiding hearth fires behind cabins. :)
I am a bit afraid that some of the hoops that I had to jump through to get here may have made performance worse, though. Please report anomalies in that regard.