Filebeat only goes to one of the Logstash Servers that is behind an ELB

might be a stupid question, but did you configure both logstash servers i the hosts and set loadbalance: true, such as:
hosts: ["logstash01:5044", "logstash02.corp.pvt:5044"]
loadbalance: true

loadbalance defaults to off, and will only send to a single logstash instance unless failed over. Take logstash01 down to see if it goes to 02. if so, probably this. otherwise i likely misunderstood your question.