Sounds like you have the situation fairly under control but just to answer your Original question yes there is a risk that your ex could have a claim over your house, once your house becomes worth something. This will happen a) if you die and the life assurance policy pays off the mortgage or b) once the house comes back into positive equity
a) isn't your concern as you won't be here! But might be of concern to your new husband if you were to marry
b) at the rate you're going this isn't going to occur for the next 10 years anyway? So not something you have to worry about in the short to medium term future.
Once the house does become worth something, AFAIK your ex would have to go to court to force a sale and this would be expensive (I'm guessing 10-20k in legal fees) so there would want to be a sizeable reward for your ex at the end of the court case to make it worth his while. I'm guessing he wouldn't do this until the house was worth 100k at least?
I'm assuming the fact he hasn't contributed basically ever to the mortgage (save a few months at the start) would have to be taken into account by the Judge if such a court case did arise-But that's just an assumption on my part. If he paid 30k towards the deposit or paid the legal fees or tax for the purchase etc that would obviously be taken into account as well if a court case did arise.
So I'd say until the house is back in positive equity, and well back into it at that you don't have to worry about him upsetting the apple cart. And hopefully by then both he and the bank will play ball and let you transfer it into your own name.
I don't know anything about side agreements but you could try this guy if you haven't already:
http://www.lawyer.ie/property
Try to stay on good terms with your ex for the next 10-20 years is the only thing you can do otherwise really. You can't plan for changes in either of your personal circumstances that could force things to a head either