I am writing this as a follow up, as 5.2.3p3 and also 5.2.4 turned out to be crashing quite a lot. It was actually crashing not only the build but also the whole editor. A couple days later 5.3.1 appeared, but the texture bug from 5.3.0 remained.
So the last stable, relatively bug-free release was Unity 5.1.4, which we’ll probably stick with for longer. All this testing and wasted time, only to move from 5.1.1 to 5.1.4… But there are also good news, and I only discovered this today – the button-offset-on-non-native-resolution bug seems to be fixed in this version! Now, off to delete the other 6 versions of Unity to save some disk space…