An update: The machine has been rending constantly for the past three days. It only takes an hour or two for the artifacts to show up, so when they did I killed the rendering, made changes, and tried again.
You may notice that I'm going to be hedging almost all my statements here: probably, likely, seems like, etc. It's all been a game of probabilities; I feel like I've been chasing shadows try to pin this down.
First, I was able to narrow down the problem to a single population. (I think.) It was a low-poly wildflower population that I copied from an old scene. On closer inspection in Blender the model itself turned out to be fine. The roughness was a little low but hardly what I would call reflective. Normals all good, etc. Removing it from the scene eliminated the artifacts for several renderings in a row. I exported it again from SpeedTree, raised the roughness to 0.8, and put it back in the scene. The artifacts returned, but fewer and not every time.
Using Cubic B-Spline, as noted before, seems to help. It's rendering now with Narrow Cubic and so far, so good. I'll try other filters to see what happens.
Turning off Anti-aliasing bloom also seems to help. I did that with the filter set to Mitchell-Netravali and it rendered fine. But I only ran it once.
I don't think it's a memory issue. I've checked with Task Manager mid-render, and there's plenty of RAM available.
I'll send a note to Planetside to see if they've every seen this before. But if changing the filter fixes it, I'm happy. Time to move on.