So it seems I figured out what caused the spinning. I had to screw the trim die a bit more, so that it starts to hold the case earlier in price.
But no matter what, the .300 neck is always about 1-2mm to high, when I compare my trimmed cases with new .300 blackout cases. When I resize them again with my .300 full-length die, the neck is at the correct position.
Here are some pics -> https://imgur.com/a/Bn8NNEK