Most banks agree to be paid the mortgage shortfall over the remaining term of the mortgage at the mortgage interest rate. It is odd that they want it repaid over a shorter period.
Which bank is it? It's ok to name them, if you don't mind doing so.
The reality is that the bank can't get blood out of a stone. You could agree just to get the property sold, and then as long as you are paying what you can, the bank is unlikely to take any further action.
Would you like to give us the full figures. It's a bit unusualy, that with negative equity of €80,000, you are still paying €6,000 a year more in interest over the rent. That seems very high. If you have your figures wrong, it may make more sense to hold onto the investment.