Thanks for writing! The "Paid cutoff date" is really only used when you want to show 100% paid invoices (zero balance invoices). Most people only need to show "open" invoices, in which case you would not want to "Include Paid Invoices". If you do want to show the Paid invoices, you have the standard 30, 60, 90, 120, 180 or 360 days windows to include those invoices.
I will add your request of an expanded "payments" option to our "wish list".
It is unlikely that we would add a header section for the Statements. If possible, can you remove the word "Invoice" from your header?