Other popular quote and invoicing plugins (for example Sliced) are able to integrate with Contact Form 7 so that a quote form can collect customer details and then automatically create a quote with that data.
To assist you with your tests, I have created a complex two column Get a Quote form on my beta site using CF7.
Please let me know if you are able to provide the code to integrate this form with your quotes add on.
Please also let me know if you require any further information.
To open a new support ticket, first select the relevant forum and then click the "New Post" button. Example: You need support for the core plugin? Click on Core Plugin support and click on the "New Post" Button.