You should improve your load balancer to support higher session rates (especially with SSL). We would be happy to pay extra money (e.g. $40, $80, $160, etc.) to have load balancers with high performance.

Currently this is a huge problem for us: we cannot scale.

At the moment your load balancers are a bottleneck and cannot handle more than 1,000 requests / s (without keep alive and with SSL enabled).

The same limit of 1,000 requests / s also applies to custom installations of HAProxy on DO... probably your hardware is not optimized for SSL and scaling the droplet / processes doesn't solve the issue.