Engine balance after new pistons

According to what I was able to find on the internet, your stock 360 pistons weigh 584 grams and the speed-pros weigh 567 grams, which is only a difference of 17 grams. I think that is insignificant and you may be able to get away without balancing on a street engine, but others may chime in.

If you do get the assembly balanced then you don't need the old pistons, but you will have to bring then a new piston, rod, bearing and rings so they can calculate the bob weight.