Thank you all for your help on this!
I followed your guidance again today, carefully following the steps, and low-and-behold, today the moire is gone when I change the resampling to either of the lanczos settings or using bilinear!
I can only assume I screwed up following the export settings. Both of the painting side images looks just fine now!
Thank you lepr, markw, old bruce and john!
I would LOVE to have pattern-making tools on Affinity Designer! I'm a huge fan of the Affinity products and pattern repeat and pattern preview features would be a wonderful addition, as well as tools to help with getting the offsets right.
Sheila Finch got a reaction from markw in Image has swirled pixels when exported for internet
Sheila Finch got a reaction from debraspicher in Feature Request: Pattern Tool/Maker