I've moved this post to the Server Admin section of the Community where you are more likely to receive a helpful response.
I know I've worked with some users in the past who have built their own load balancers (braver souls than myself) which is an option as well.
We've used Zen load balancer on our smaller Tableau Server instances. We aren't doing any fancy stuff on those like we are with our F5, so I'm not actually familiar with other functionality that the product provides. But I can say they've worked well for simple traffic routing, and users haven't had any issues using Tableau Server through them.