Man, was Unreal Engine always full of these graphical bugs? Ever since I adopted the engine back at launch, every version had a feature broken by an update. Makes me wonder what UDK was like, especially when some of these bugs didn't exist in the older engine.
Turns out this is a known issue: https://forums.unrealengine.com/unreal-engine/feedback-for-epic/106544-dynamic-shadows-artifacts?133869-Shading-problem-in-4-14=&viewfull=1