Alex,
From the pictures you posted of your pistons, the scoring doesn't look to be too bad or on the thrust faces. If they were mine, I would try carefully filing away the areas that have 'picked up' to remove any high/hard spots. When pistons pick up like this, the surface gets contaminated with material from the cast iron cylinder - likewise, the barrel will be contaminated with alloy from the piston. It is imperative that this is removed otherwise it will only pick up again. Any alloy adhering to the bore can usually be removed by lightly honing the bore or by using 400 grade wet and dry paper. Whilst dealing with the pistons, make sure the rings are still free in their grooves ( the alloy may have been drawn over the rings - trapping them in the grooves).
Regards,
Eddie.