It'd be really helpful you could add the following improvements:
-Add a new billing method to projects that could be called: "Fixed Bid" or "Based on a Fixed Amount"
-When creating an invoice for a project that has that billing method, the form would require user to enter an amount, thus; the invoice wouldn't show hours but a single line for the project with a single amount.
-The billable / non-billable and/or approved / not approved hours, are merely for information, stats, tracking, etc.
It'd be even better if you could include in the project's dashboard a new indicator to show "billed / budget" amounts comparison