WooCommerce Private/Hidden Shop and Menu

Overview
I have a client that would like to have a WordPress site with a WooCommerce shop visible only to registered clients.

Specific requirement
The shop and all the products, cart, shop menu items needs to be completely hidden unless the user logs in with their registration information. It is very important that there are no shop links on the site (or evidence of a store of any kind) unless the user is logged in.

A hidden link (or unlisted URL preferably) would allow clients to log in and gain access to the WooCommerce shop.

Once the user logs in, the additional menu items for products, cart, etc., should be visible.

Why do I want it this way?
My client sells their product wholesale to retail stores and has agreements in place not to compete with them. They still want to advertise the products, but have a page dedicated to “Find our products at these retailers…”

A proper shop needs to be available once clients log in so they can order their products from the wholesale part of the store.

Why WooCommerce?
My client really likes what the shop can do (and so do I), but I cannot figure out how to get this to work with WooCommerce, or if it is even possible. I tried contacting WooCommerce directly, but they were less than helpful in finding a solution for me, so I am trying the expertise here.

Search results so far
In my search across the net, I have found nothing that answers my requirements above. Most solutions suggest showing the shop as normal but redirecting requests back to the home page. This is unacceptable. The client is explicit that there be no shop links visible unless logged in.

Any suggestions?