Most of that is a premature optimization IMO.

First of all, are you sure you are targeting the right market?

I've worked with fashion companies with similar price points as the OP. At that price, many people expect heavy branding or very good quality.

Since you're looking for a quick win, you should put your focus on improving the product pages. Your selling point is the product's quality. You need to emphasize the product features on every page. You currently only have a few sentences on each one. Also, you have a great opportunity to tell a story with sourcing the product from artisans in Italy.

I see too many people jumping into conversion rate optimization when they don't have their base marketing strategy figured out.