Hi Maxim,
Thanks for the reply.

What about if we used a stream/tcp proxy_pass with resolver? Something like this:

resolver 8.8.8.8 8.8.4.4 ipv6=off;

stream {
server {
listen localhost:81;
set $upstream_host my.upstream-host.com;
proxy_pass $upstream_host:443;
}
}

server {
listen 80;
location ~ /api/ {
rewrite /api/(.*) /$1 break;
proxy_ssl_verify off;
proxy_pass https://localhost:81;
}
}

Would this work?
Thanks,
Max