A lot of people will have these same problems without realizing why. You need to evaluate your cutting procedures first. Cleanliness is the biggest problem, you do not want cross contamination of grit sizes on your laps. So the first thing to do is CLEAN all your laps (soap & water) and also thoroughly clean your machine. Always use new, clean tissues/towels with each lap and clean the stone and machine when done with that grit size. When going from one lap grit to the next make sure you’re taking enough material off to eliminate the previous grit scratches.
You may be doing this already, it’s just a checklist to be sure. I know the feeling of frustration with scratches showing up or not being polished out. If you get a new lap DO NOT charge both sides of the same lap. This will invite contamination and will be a never ending source of frustration for you. Try cleaning everything first before investing in a new lap, no sense spending money if you don’t need to.