So I had this problem while I was designing the landing page for month17.com (disclaimer: that's my domain). What worked to not let it look like complete AI slop was using other landing pages that look good as "inspiration" for the model, through providing screenshots which yields sufficient results, in my opinion.
it looks identical to god knows how many other sites and also uninteresting for the same reason. How would catch attention of a customer? With a card slightly rotated over another? That's abysmal
I would be curious as what you would consider an example of good design, then I can see how far an agent gets with that. In any case, contrary to what you might believe, this landing page does convert pretty well.
To start with would you be willing trying inputing Claude with the following instructions? No rounded borders, no excessive padding/margins, no rotated cards, no excessive shadows. More compact/dense ui but also increase base font size a little bit. Make the dark ui the default, use a less neon green color on dark mode, contrast is not great, same for the foreground color. A little nit: On mobile there's an annoying horizontal scrollbar.
Maybe you have fun saying if it converts better or not! I'm fan of a/b testing