Here are few settings to play with, if you haven't already
- set refresh_interval to -1 for the dest index. Once reindexing completes set it back to null.
- See if increasing index_buffer_size helps https://www.elastic.co/guide/en/elasticsearch/reference/current/indexing-buffer.html
- Set replica of the dest index to 0. Once reindexing complete set replica to whatever you want.
Even if none of these work, please post your findings. It will help others.