Sinatra/Nginx/ELBv2 API is generating ERR_SPDY_PROTOCOL_ERROR on Chrome 58 or higher only

I have an API with the following stack:

Sinatra <=HTTPS/TLS=> Nginx <=HTTPS/TLS=> ALB(ELBv2)

It's a basic URL shortener that sends a 301 redirect to the browser to go to the longer URL. This was working flawlessly for a year or two, but since Chrome 58, I now get ERR_SPDY_PROTOCOL_ERROR on redirects from the API in Chrome. Regular pages return just fine, and other browsers work fine. The reply is definitely sent by the ALB, as I see traffic flow, and there's no errors reported in CloudWatch or in the logs for either Nginx or Sinatra.

I've opened a ticket with AWS Support, but I haven't gotten much useful from it. Has anyone else seen something similar? I'm not even sure what to try to fix this, since my nginx isn't even configured to use SPDY or HTTP2.

EDIT: Here's an ALB sample access log for the broken attempt and a working (via curl):

h2 2017-06-21T15:30:01.438546Z app/aws-example-net/019315b3036f76ac 184.75.37.61:59367 10.252.14.202:443 0.000 0.004 0.000 301 301 30 1170 "GET https://aws.example.net:443/short/-OpLPG8h HTTP/2.0" "Mozilla/5.0 (Macintosh; Intel Mac OS X 10_12_3) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/59.0.3071.104 Safari/537.36" ECDHE-RSA-AES128-GCM-SHA256 TLSv1.2 arn:aws:elasticloadbalancing:us-east-1:XXXXXXXXXXXX:targetgroup/ecs-prod-e-urlshortener/7c6cddcc83c91aeb "Root=1-594a90f9-41b321bf039f142a083cb587"
h2 2017-06-21T15:30:06.928711Z app/aws-example-net/019315b3036f76ac 184.75.37.61:19376 10.252.14.202:443 0.000 0.004 0.000 301 301 46 1170 "GET https://aws.example.net:443/short/-OpLPG8h HTTP/2.0" "curl/7.50.1" ECDHE-RSA-AES128-GCM-SHA256 TLSv1.2 arn:aws:elasticloadbalancing:us-east-1:XXXXXXXXXXXX:targetgroup/ecs-prod-e-urlshortener/7c6cddcc83c91aeb "Root=1-594a90fe-2f1b92043fe3030461e84219"

EDIT 2:

Sanitized example output from curl -vvv:

https://pastebin.com/Ws553Mxj