Hi Matt Edwards and welcome to the forum!
The thing about subitting to a database from InfoPath is that the form's Main DOM must be based off of the database for this to work. So you have to design the form with this in mind from the beginning - you can't add it later. I would say that you could use our Database Accelerator product to have the web service submit into your database, but since you're running Access, that won't work either.
So the only thing I can think of is to create the form with the Main DOM based off of the database schema, and then add the button to submit. You could re-create the entire Project Request form, or maybe you could just make the schema exactly the same in the new form you create to submit to Access so that you could just open the XML files in both templates, and then just submit with the other form.
Sorry if this isn't very helpful - please give a few more details so we can give more specific advice!
Matt Faus / Microsoft InfoPath MVPQdabra® Software / Streamline data gathering to turn process into knowledge