either they want your money in the manner you are offering or not at all.  They get retrieve that crazy amount of information from their side when they issue the invoice - they should include that information.  If they have provided you with the correct bank information then there is nothing you can do.  Realistically sending back the banking information to them is ridiculous as this is provided by them to set up PAP/ACH payments. 

I'm not sending their bank information, just their internal account number. Sage doesn't use account numbers for either payables/vendors or receivables/customers, but its necessary to use in some cases for payments to vendors. It's required to use when paying through a bank portal for instance, so they know where to apply the payment against for their receivables. 

you can send them ACH verification which has the invoice numbers associated with payment on them.  You need to send them receipt from payables modules 

Nearly all of my vendors are paid by EFT and are emailed the payment reports. However, some vendors that only send statements often don't have invoice numbers. So I create my own invoice number (using the statement date), but if the payment report had a field for the vendor's account number, that would be helpful. This is often utilities (phone, gas, hydro) but not always. I've had utilities misapply payments and this is a clear way for the phone company to apply my payment against the appropriate customer account (mine).

are they are on pre authorized through your bank? if so the current debit to your account would be your current invoice you received and would never pertain to one that is 30+ days