The way to do it seems to be to share the files from the source account to the destination account, copy the files in the destination account and then remove the files from the source account.
Sharing the files with the destination account and then removing them from the source account results in them being removed from the destination account.
Sharing the files with the destination account, adding them to My Drive in the destination account and then removing them from the source account results in them being removed from the destination account.