I have tried changing the fullsize image size under appearance - settings and then running the Derivative Images plugin but they stubbornly stay huge and blurry.
The “huge” size is coming from your CSS: there’s several styles at the bottom of the “slick.css” file from the Connected Carousel plugin that are forcing images to stretch to fill their containers… those styles look like they were added after the fact and don’t come from the plugin itself.
As for the thumbnails not increasing in size with larger constraints, it looks to me like, at least for the example item you gave, you actually imported very small thumbnail images in the first place. Omeka can’t resize the thumbnail to be bigger than the source material it has access to (at least, not in any useful way).
For example, the metadata would seem to indicate that one of the images is sourced from here and as you can see it’s already a quite small thumbnail. You’d need to replace these with actual full-size (or at least larger) images to have Omeka be able to create any better thumbnails. Or, if you’re fine with them being small but just want to remove the blurriness, fixing the CSS as I mentioned above will handle that.