I am having the exact same issues.  This is really ludicrous that we can not add an existing invoice to a project.  To delete an invoice and then redo and change the invoice is illegal in our accounting laws, this is really not an option.

Its a basic functionality that is required of using a projects function..... surely this is now years on and this has still not been resolved.  

We do hundreds of quotesd and can not possible create a project for every singel quote... seriously .... ...