Well, for these particular images, it looks like rotating the weave 10 degrees and exporting to JPEG is the solution that works if I use Affinity Designer. I tried exporting to PNG without rotating the weave and the resulting images had the same wavy lines.
It does seem odd to me, however, that the original image files are JPEGs and they display the horizontal weave without distortion.
For shits and giggles, I resized the original images to the desired dimensions using Apple Quick Actions and the images are perfect (although I have to see if I can edit the actions to save using progressive compression).
Thanks to everyone offering up ideas!