I got those same marks on my old 335i after it came from the paint shop. The paint shop told me the car was covered in some plastic to prevent dust from touching the car etc. and it dried on the car while under the sun by mistake in some areas. They had to buff it out for me several times, similar to OP's method...
AWE NR | SWIFT SR| PAGID RS29 | RE71 R | 6MT