Autoscaler cooldown too long

A flash sale drives a fast 6x ramp over ~3 minutes. Your autoscaler is healthy, metrics are fresh, and it IS scaling up, but too slowly to keep up: it adds a small fixed number of instances, then waits out a 300-second cooldown before adding more, so it takes ~15 minutes to reach the capacity you need while users get 503s in the meantime. Instances boot in 90 seconds, so boot time isn't the main lag. How do you triage and fix the scale-up rate?