Hey,
I can make a website which will be integrated through Amazon, Ebay, Shopify and Big Commerce having integration of openCart or other Cart plugin with Paypal payment integration. I am having myself experience of Ecommerce Website including all these integrations. I am giving you estimation time but it maybe less according to the actual requirements as what you want exactly.
My experience in ruby on rails is 2 years and I am having experience of API integrations, gems modification and other projects like trips website, ecommerce site, facebook like project etc.
Lets discuss the complete requirements on message so I can give you actual time estimate.
Best Regards,
Arslan