Reduce AWS Load Balancer health check delay

When I make a deployment to my Fargate service, the new containers experience a strange 3 minute delay when registered with the Network Load Balancer. The new HTTP Targets are taking exactly 3 minutes to go from Init to Healthy, even though the URL the health check calls becomes operational before the 3 minutes begin, as verified using the container's public IP.

I changed the health check parameters from defaults to allowed minimums, but this delay didn't change at all.

The health check grace period is 0, though that seems irrelevant as it relates to ECS not the Load Balancer.

Is there a way to remove or lessen this wait?

FYI, I posted this question on ServerFault and got no answer in 10 days https://serverfault.com/questions/1161525/reduce-aws-load-balancer-health-check-delay