Sticky one MabelQ.
So your ex doesn't have a job or any savings. He sounds like he's unlikely to be applying for another mortgage anytime soon then. He probably doesn't care about his credit rating being affected so?
So although you can threaten him with that, he may not care.
You could just reduce your mortgage payments for a few months and shake him up a bit. Then go back to full payments & pay the arrears off ASAP. That's what I did. 1 month of missed payments was enough to make my ex crack.
In your case the rent from your family, even though it's 200p/m below market rates, covers the mortgage. That's a great position to be in. So what's coming out of your own pocket is the LPT, house Insurance etc. You say this amount is approx 100 p/m.
One route you could go as has been discussed already is you reduce mortgage payments to the rent you receive minus the shortfall. You will fall into arrears. However if you go down this route the negative equity will never be paid off. You'll be stuck in this limbo forever. I think it's one way to go to see if it can force your ex to sign the Deed of Assignment (by the way I know nothing about these I assume they are legally binding?) but I don't know if it's of much use to you as a long term strategy.
Re the TRS. Whatever about pretending it's still your principal private residence, you are definitely not still entitled to claim TRS for your ex. Your TRS should have halved when he moved out. If he applies for a social welfare payment like rent allowance they could detect that he is already registered for TRS on your house, then you'll get a letter from them looking for that TRS to be paid back (as has happened to me and others on here). If he's out of work this sounds quite likely to happen?
Where are you getting your valuation data for your house from by the way? Are you sure it's accurate?
Not that I'm encouraging landlords to rent out shoddy properties or anything but are you sure you'd have to spend as much on refurbishments as you think in order to rent out your house? Renters in the main cities anyway are desperate these days.
Because you could also go down this route: get your family out, do a patch up job on the house, register with the PTRB, sort out the TRS and rent the house out for full market value. Your mortgage will go up due to changing the TRS status (but TRS has reduced a lot anyway have you checked exactly how much it's worth to you per year?) and the cost of registering with the PTRB. But you'd be getting 200 p/m more in rent. This means you could pay the mortgage, LPT, Insurance etc fully from the rent and the house would have no net cost to you. Then you bide your time until the house is out of negative equity and ask your ex if he's willing to sell.
You mention forcing a sale of the house by the way. From my research into this, you're back into 15-20k court case territory in order to force a sale. So you'd have to get your ex to agree to a sale. By the sounds of it he might want to wait until the house is not only out of negative equity, but actually worth something before selling so that he gets something out of it. It's very hard to predict what will happen with property prices but it could be years before the house is worth something, if ever (there could be another crash). So you have a big problem on the horizon regardless of what avenue you take to cover the monthly costs in the meantime.
From what I know - correct me if I'm wrong anyone - neither you nor your ex can force a sale unless you go down expensive court route. The only way to force a sale is actually to go into arrears to the point where the bank repossesses and forces a sale. Do you have any idea/estimation how long it might be until the house is out of negative equity?