If you have pyrite the chances of you getting a new mortgage is very limited. You might want to rethink clearing the mortgage. Also Ulster Bank have said they will still offer top ups as they have not fully left the market. Check their website.
Also have you been accepted the the pyrite scheme? I know of a few families where they have a one off house on a site where repaired. Bathroom and kitchens where reinstated. If they wanted a new kitchen bathroom etc they had to pay extra for this and paid someone else to install the kitchen. Foundations were repaired.
If pyrite has been noted in the area then maybe ask for a top up but do not mention pyrite in your conversations. Check what you need to complete your house and approach Ulster Bank.