Flask & NGINX performance tuning - performance

Question

I have a RESTful web service written with Flask framework.
To make it simple, let's assume that all requests are GET, that is only request line + headers.
Request buffering time usually takes about 100ms, processing time - 1 second/request.
During stress tests I found an issue:
When lots of clients (hundreds+) open a connection to it at the same time, there's a delay between connections opened and start of processing.
It turned out that Flask reads a headers part of HTTP requests upon connection. More connections -> more headers to read -> bigger networking load -> bigger request buffering time.
For example: 100 simultaneously opened connections will start buffering together and will take 0.1*100=10 seconds to buffer. They will then pass to processing stage together.
My intention is to reach 2 goals:
Primary: Start processing as quick as possible
Secondary: Buffer all requests as quick as possible
Despite a seeming contradiction, both of them can be achieved by preserving a rule:
Buffering less connections, if there's a processing starvation.
Once again, to make it simple, I want my server to buffer only 10 connections at a time (/second). All the other connections should be accepted by server socket and wait patiently for their turn. Alternatively, accept only 10 connections/second (and still wait for others, not to discard bursts).
I tried to do it with NGINX reverse proxy with limit_req:
http {
limit_req_zone $server_name zone=processing_limit:10m rate=1r/s;
}
location ~ /process {
# Limit requests
limit_req zone=processing_limit burst=1000;
include proxy_params;
proxy_pass_header Server;
proxy_request_buffering on;
proxy_buffering off;
client_max_body_size 100m;
proxy_pass http://127.0.0.1:8081;
}
But NGINX also buffers all connections together and only forwards 1 request/sec to a backend server.