This seems kind of roundabout. But it would do the job.
1. Create a custom object that has all of the fields that you want from the project properties page.
2. Create a mapping from the project object to your custom object and then a second one from the custom object to the project object.
See this thread if you need instructions on how to do this: Convert Clarity Idea into Incident
3. Create a process that converts your project to a custom object using the Convert Object System action.
4. Create a second process that autostarts on create of your Custom Object that converts the custom object into a new project. You could also probably launch a subprocess from your previous process to accomplish the same thing. But a second process seems more straightforward to me.
Jeanne