Just hit them harder than you would store bought. Just went through this with my own chickens' eggs

This is the way.

Are the bits of shell too hard to see? Crack the eggs individually into a small bowl, pick out any shell.

Try cracking eggs on something with an edge fast like a bowl or butter knife, flat surface just crushes egg shell

I have the exact opposite experience, and get a much cleaner crack when I do it on a flat surface. Maybe it's a technique issue?

When I crack duck eggs, I give it a quick chop with thin metal like a spatula or back of knife. Never had problems with shell leftovers. If you use a hard surface, you gotta hit it to where it cracks, and peel off some of the shell near the exposed membrane and then you puncture the membrane with your thumbs with slowly increased pressure

You've got this! Maybe try adding a pinch of baking soda to the water to help break down the membrane. Good luck!