Great writeup. It's cool that they were able to figure it out as quickly as they did, all things considered.
If I were brought in as a consultant on this, my first question would be: why are you using a fleet of HAProxies instead of the ALB? I'm not saying that's a bad choice, but I'd want to know why that choice was made.
The second question I would ask is what kind of Chaos Engineering they are doing. Are they doing major traffic failover tests? Rapid upscaling tests? Random terminations?
Those are probably the first two things I'd want to solve.