Shipping alternative for shops selling one-of-a-kind items

[greathouseshop]

I am an interior designer with a Shopify store to sell our inventory of vintage items and antiques.  They vary in weight, size, condition, value, etc. and every item is a one-off.  I can't lump them into the few vague shipping categories available.  Is there a way to eliminate shipping completely? I.e., a "request shipping quote" option so we can arrange and bill the S/H separately?  I would assume there are plenty of stores like ours (not dropship, not multiples) who need this kind of fulfillment.  Please provide work-around's if you have them.  Thank you!

I have chatted with customer service about this and they couldn't provide a meaningful solution.  They did escalate the request, so I am waiting for a supervisor response.