Select Questionnaire Type After Project Is Made

The process for my company is to have a phone call, send invoice for initial consultation, and then send questionnaire. I set up the client the project board when we send out the invoice. At that point the questionnaire is already preselected by the system and I can't go in and change it. I have talked to the support staff and they say all we can do to select one of our questionnaires for a client is to first send a project request to the client. Then the client creates a project board that I can then attach an invoice.

We all onboard differently and I am just requesting that there is an option to set up projects first and have the option to select which questionnaire we would like to send them later. A simple drop down menu like they have on the "invite a client" portal would be great.