Eureka support other forms of fixed addresses. such as ENI and Route53 DNS (which in EC2 vpc can be private). In all cases (EIP or otherwise) you can secure your service with Security Groups.
See https://github.com/Netflix/eureka/blob/master/eureka-core/src/main/java/com/netflix/eureka/DefaultEurekaServerConfig.java#L664 where you can supply the binding strategy via eureka.awsBindingStrategy=...
Thanks.