Thanks to everybody for their help with this, especially Russell.
After much trail and error, I finally managed to get Gigapixel AI working. However, it involved uninstalling Topaz Studio beforehand. When I then re-attempted an export in Gigapixel, my firewall threw up a strange message asking my permission to let Gigapixel modify the output image, to which I said yes — and voilà. There it was, finally, in the specified destination folder. I tried with other images, and they exported successfully too. I’ve since reinstalled Studio, and both programs are working concurrently now.
To be honest, I’m still not sure what the problem was specifically, but there was evidently strange conflict between Gigapixel, Studio and my firewall. Nonetheless, I’m just pleased that the issue’s resolved itself, and hopefully the paragraph above can help others who may experience similar down the line.