Custom Shopping Experience w/ Zen Cart Back-end

I am currently building a completely customized website outside of Zen Cart. My site is a very customized experience for purchasing instrumental music a.k.a. beats. From the screen(s) I am building, a customer will be able to search/filter beats, listen to beats, add to cart, remove from cart, clear cart and view cart.

I am looking for a shopping cart product to use as the underlying cart and I am looking at Zen Cart. So actions like add to cart, remove from cart, clear cart and view cart I am envisioning as ReSTFul API calls to Zen Cart. Once the user is ready to checkout I would like to then transition the customer over to Zen Cart and let Zen Cart walk the customer through the whole checkout experience. Once payment has been finalized Zen Cart would then email download links to the customer.

Would anyone be able to advise me at if this is at all possible using Zen Cart?

You can use Zen Cart as your primary solution. All of the customized pages you are making 'outside' of zen can easily be added to the zen fold. Takes a bit of time and an understanding of what to change.