Convert Our Current Custom Website to Wordpress or Better Suited Platform

We currently have a subscription based clothing website where customers can: a) purchase a membership (and are then billed monthly) b) purchase individual items from our online store (one time purchase) It's really that simple. For years we have been using a custom website platform (mysql) custom cms for our website which must of course do all the things a shopping cart must do, such as order history, login account information, shipping address - and receipts on every recurring charges that are successfully processed every 1st of the month (for members) - The website is adapted for web and mobile platforms. We do not have an app yet, but plan on adding one in the future. Payment Processors = We currently use both: a) Paypal b) Braintree The reason we are posting this job is because we wanted to add a feature to our current website that will allow our customers (members) to customize their own box, as opposed to only receiving the surprise box we send them every month. While thinking of adding this feature, we decided best to update entire website (similar/if not same) design layout to Wordpress or another system that will be able to offer us a more universal way to scale without having to add further coding to our custom website. So we figured if we hired someone with experience that can convert our current website and add the new feature to the new website we can complete both tasks in one project. We would require a fully converted website with all of its existing features (which some might have glitches) auto cron emails to be triggered, mail chimp added to our website to better manage customers and visitors. Basically what our website currently has plus things you can suggest all ecommerce websites must have to be search engine friendly. All tied into our social media pages and giving us a better loading and overall browsing experience for our customers. We are also attaching for your review a snapshot of what the custom page would look like, once as a MEMBER you would sign in you would be able to piece your own outfit together selecting the items of your choice. This project must be completed within 3 weeks from date of this posting and ready to go live after thorough testing for August 1st. We will provide all design and photos we would only require you to put together layout and the coding part.