Last time I shifted a large record collection I had double walled cardboard boxes custom made cost was not much more than regular boxes.
Trick was to keep the boxes smaller in terms of numbers of records so that they are easy to lift and additional rigidity when stacked.
Successfully moved across country on pallet with no issues ( shipped as top stow only - nothing on top ). You can get pallet crates if you cannot trust your shipper to not stack anything on top.