Elasticsearch reindex - self-hosted to AWS - timing out, consistently failing

I have a set of what I presumed to be fairly small elasticsearch indices in a self-hosted cluster of ec2 instances. I'm in the middle of trying to migrate this date into an AWS-managed elasticesearch cluster, and I've been having trouble getting the reindex tasks to consistently reproduce the documents in the target cluster.

My cluster has about 330,000 documents in it - my approach has been to expose the source cluster to the destination cluster and to issue a reindex operation to the destination cluster, using some scripts written in ruby:

  def reindex(index:)
    logger.info("reindexing #{index}")

    task = dest_es.reindex(
      body: {
        source: {
          remote: {
            host: source,
            username: source_username,
            password: source_password,
            socket_timeout: '5m',
            connect_timeout: '30s',
            external: true
          },
          index: index
        },
        dest: { index: index },
        conflicts: "proceed"
      },
      refresh: true,
      timeout: '3m',
      wait_for_completion: wait_for_completion? # set to false by default
    )

    logger.info(task)
  end

This task, however, never reindexes 100% of the documents, and frequently times out with the task status stating:

{
  "completed" : true,
  "task" : {
...
    "type" : "transport",
    "action" : "indices:data/write/reindex",
    "status" : {
      "total" : 317554,
      "updated" : 0,
      "created" : 184000,
      "deleted" : 0,
      "batches" : 184,
      "version_conflicts" : 0,
      "noops" : 0,
      "retries" : {
        "bulk" : 0,
        "search" : 0
      },
      "throttled_millis" : 0,
      "requests_per_second" : -1.0,
      "throttled_until_millis" : 0
    },
    "description" : """
...
""",
    "start_time_in_millis" : 1660058838837,
    "running_time_in_nanos" : 312625819581,
    "cancellable" : true,
    "headers" : { }
  },
  "error" : {
    "type" : "socket_timeout_exception",
    "reason" : null
  }
}

If i try to break this reindex operation into multiple tasks, running asyncronously, i can issue a number of async tasks to reindex, say, 2000 documents at a tim. . By looking at POST /.tasks/_search it seems that they all complete without issue, but I still can't quite get to 100% - in fact the total number of docs varies between 60% and 99%

Are there config settings that are generally used with reindexing across clusters? I feel like this should be a lot more straightforward than it's turning out to be.

Thanks!