A few thoughts
1) If you are under no pressure from Start, then staying in the house seems like a good idea. The interest on the mortgage is around €12,000 a year. You are paying around €5,000 a year, so your mortgage is increasing by around €7,000 a year.
But so what? It does not look as if you will ever be in a position to pay it, so it doesn't really matter whether your negative equity is €130,000 or €137,000.
Over time, house prices might increase and eliminate your negative equity.
2) If Start agree to write off the shortfall, then an agreed sale might be the way to do. Then when you or your spouse start earning again, you will retain your savings rather than give them to Start Mortgages.
3) If you are planning on returning to the UK, you should defintely do an agreed sale first. It makes your bankruptcy a lot easier to deal with
4) If you are planning to stay here, go for an agreed sale. If Start don't agree to write off the shortfall, go for a one year Debt Settlement Arrangement.