You could possibly do one thing.
1. Setup a Category with Sub cat and products in it.
2. And all products listed in it, you can enable for COD (cash on delivery), and no shipping required. with product amounts set to the lowest denomination possible. such as $ 1..
3. And let the users, visitors, just select the product, add them to the cart, and submit it. (however make sure this is available only to registered users.not guest checkout.
4. Once the orders start pouring in, you have the email id of the user and the list of orders (just document them) and prepare a quote and push across an email to the user with an offer, with a link to the final pricing and product if you need it to be.
Note :So when you process the request from user, you will also create a new product on the shop with the total price, and products included in it. and send the products direct link to the user in the email .
Do let me know if this sounds logical... I have never tried or done it.. it's just a thought. it should work.
Let me know if you looking for something else, cuz for now i don't see any modules on AbanteCart cart that can achieve this requirement directly.