Yeah if you’re getting a container to move your life then having them in there is going to be the cheapest overall way, any other transport method will be extortionate. Just be sure to pack them really carfefully in good quality shipping boxes. Just like you would to move house but more carefully again!
How permanent is the move? If it’s temporary (i.e. a couple years), take your top 20-30 records and then store the rest in a climate controlled storage unit.