Make sure that the top of the seat-tube is not crimped inwards from previous attempts at cranking down on an undersized seatpost. Remove the seatpost and binder-bolt and carefully look at the slot in the tubing, both sides should be straight and parallel.

The zig-zap scratches on the post is a sign that the top of the seat-tube is actually crimped inwards. The points at the top on each side of the slot is then aimed inwards, scratching the post. This also reduces contact surface area between the post & tubing, it's just pinched at the top and isn't in contact anywhere else. To fix, stick a big flat screwdriver down into that slot and pry it apart so that it's slightly bowed outwards. This will then let you measure the true ID of the seat-tube about 1.5" down from the top. Use precision calipers. Then get a seatpost of that diameter.

When you slide the post down about 2", you SHOULD NOT be able to rock it back & forth with the binder-bolt removed. Then with it fully inserted to operating depth, it takes minimal pressure from the binder-bolt to hold it in place. I suspect that the true seatpost diameter you need is probably closer to 26.2 to 26.6mm.