Is there an app that integrates with Shopify where you can email your customer a quote that is within Shopify or can be paid within Shopify?
Also where the customer can maybe edit the quote to add products or change quantities?
You can give a try to this app : https://apps.shopify.com/request-for-quote if it fits your needs, If not then we can find a way around with a custom app to achieve you requirement.
Let me know what you think after trying this app.
Cheers!