Hosted vs self hosted ecommerce
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Ive always done self hosted and never had any problems as long as the site is probably optimised (magento can easily be hell if it's not setup properly)
Make sure everything is fixed and start promotion. It should do well if you already have the best content.

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With e-commerce it really is about creating the best layered environment for your products and getting as much link juice for them. I think self hosting with full control is really the best option. I use Wordpress, woocommerce and infinite SEO, this allows us to integrate a very powerful affiliate environment which ensures loads of direct links to the products.
Look at environment like amazon, everything's self hosted, right down to reviews. You need everything on your domain. Simple
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I don’t really think it will be simple enough to rank better with a website that contains all the images on some other server. It might help you with site load time but if the CDN is not SEO friendly probably you will see a dramatic fluctuation in rankings.
I would highly advice you to use self hosting ecommerce website and then properly optimize it according to the SEO standards in order to rank better in SERPs.