Playing around with the tool a bit, supersampling seems to work pretty well to avoid those artifacts. (Thanks to the speed of Fast Style Transfer, this is feasible.)

EDIT: There's a catch. The checkpointed models are calibrated for smaller images, so you'll get better styles with smaller images. Larger images tend to just have images repeated: https://twitter.com/minimaxir/status/793161755992002560

I hadn't seen that, thanks for the link - it looks useful! Right now the kernel size is not divisible by the step size - I'll try changing the transformation network.