Unfortunately, moving to a subdomain won't help SEO vs a blog on a TLD-- due to abuse in past years, Google now treats subdomains as separate entities and you won't get any lift from it.
Shopify can be optimized very well for search engines, but rewriting theme code with an understanding of SEO best practices is critical. You might miss out on the vast wealth of WordPress plugins for added functionality on a WP blog versus a Shopify blog, however.