There is absolutely zero reason why they can't send the money again. You don't need to wait till next pay day, nor would that mean a double pay run as Jamiegray suggests.
The payroll has been run and all tax/ni accounted for in her pay this month. All you are needing is the net pay. As far as the company is concerned the money was sent, so they think everything balances their end.
The letter and correspondence from the bank shows the money didn't arrive due to an input error on your g/f's bank details. All they need to do is resend the same amount with the correct details this time and liase with the bank to get the money in their suspense account back, everything will balance again.
The only problem by the sound of it is, being a big company, you just haven't found anyone high enough yet to make the decision.