I'm just a user, but trying to brainstorm:
if you don't use the "Collect on delivery" payment option you could change the words to "Quote Request", so they enter the order, but the payment method is "quote request".
or
with the cart option, the customer can place the items in his or her cart, then go to the accounts page and name the cart such as "Quote Request for H.R." you can see all the carts back-end. The carts have not been processed yet, but you can see exactly what they are requesting a quote for.
I haven't tried either of these, my site is down