How many peptides are on your list? Would it make sense to test the binding in vitro?
MircoScale Thermophoresis (MST) is an easy, fast and precise method to investigate biomolecular interactions. It consumes very little sample and could therefore be very helpful for your project. This method will allow you to also obtain binding affinities, so you can also rank your peptides for highest affinity.
Following this link, you will find a lot of publications where MST has been applied to study protein-peptide interactions: