Identifying bottleneck with nginx VPS load testing

Question

I'm trying to optimize a Digital Ocean droplet (512mb), testing using loader.io

I'm testing on my homepage, which is HTTPS / PHP. I setup FastCGI page cache, which got me from 100 req/sec to 2,000 req/sec.

But anything beyond 2,000 req/sec is resulting in a lot of timeouts and slow responses (goes from 20ms average to 1500ms average). I'm trying to identify the bottleneck. It's not CPU/memory yet, because load barely reaches 0.30 and memory usage is about half. I tried resizing to a much bigger droplet, and the timeouts still happen.

It's not FastCGI because the load testing performance is nearly identical on a basic .html file.

During the timeouts, error.log is empty. Nothing seems to be throwing errors (that I can find). Kern.log has this log:

TCP: Possible SYN flooding on port 80. Sending cookies.  Check SNMP counters
TCP: Possible SYN flooding on port 443. Sending cookies.  Check SNMP counters.

I tried disabling syncookies, which stopped those errors, but the timeouts still persisted.

During the timeouts, I start seeing a buildup of TIME_WAIT:

netstat -ntla | awk '{print $6}' | sort | uniq -c | sort -rn
   6268 ESTABLISHED
    831 TIME_WAIT
      6 LISTEN
      2 FIN_WAIT1
      1 Foreign
      1 established)

My question is, where else can I look to determine the bottleneck here? Are there other error logs or commands I can use to monitor?

Here is my nginx.conf (FastCGI and regular browser cache are in my default file). I've tried multi_accept, which seems to worsen the timeouts. I know worker_connections is ridiculous, but it doesn't seem to matter how much I raise or lower it:

user www-data;
worker_processes auto;
worker_rlimit_nofile 200000;
pid /run/nginx.pid;

events {
    worker_connections 200000;
    # multi_accept on;
    use epoll;

}

http {

    ##
    # Basic Settings
    ##

    open_file_cache max=200000 inactive=20s;
    open_file_cache_valid 30s;
    open_file_cache_min_uses 2;
    open_file_cache_errors on;
    server_tokens off;

    sendfile on;
    tcp_nopush on;
    tcp_nodelay on;
    keepalive_timeout 30;
    types_hash_max_size 2048;

    include /etc/nginx/mime.types;
    default_type application/octet-stream;

    ##
    # Logging Settings
    ##
    access_log off;
    # access_log /var/log/nginx/access.log;
    error_log /var/log/nginx/error.log;

    ##
    # Gzip Settings
    ##

    gzip on;
    gzip_disable "msie6";

    gzip_vary on;
    # gzip_proxied any;
    # gzip_comp_level 6;
    # gzip_buffers 16 8k;
    # gzip_http_version 1.1;
    gzip_types text/plain text/css application/json application/x-javascript text/xml application/xml application/xml+rss text/javascript;

    include /etc/nginx/conf.d/*.conf;
    include /etc/nginx/sites-enabled/*;
}

Here is my sysctl.conf

### IMPROVE SYSTEM MEMORY MANAGEMENT ###

# Increase size of file handles and inode cache
fs.file-max = 2097152

# Do less swapping
vm.swappiness = 10
vm.dirty_ratio = 60
vm.dirty_background_ratio = 2

### GENERAL NETWORK SECURITY OPTIONS ###

# Number of times SYNACKs for passive TCP connection.
net.ipv4.tcp_synack_retries = 2

# Allowed local port range
net.ipv4.ip_local_port_range = 2000 65535

# Protect Against TCP Time-Wait
net.ipv4.tcp_rfc1337 = 1

# Decrease the time default value for tcp_fin_timeout connection
net.ipv4.tcp_fin_timeout = 15

# Decrease the time default value for connections to keep alive
net.ipv4.tcp_keepalive_time = 300
net.ipv4.tcp_keepalive_probes = 5
net.ipv4.tcp_keepalive_intvl = 15
net.ipv4.tcp_syncookies = 1

### TUNING NETWORK PERFORMANCE ###

# Default Socket Receive Buffer
net.core.rmem_default = 31457280

# Maximum Socket Receive Buffer
net.core.rmem_max = 12582912

# Default Socket Send Buffer
net.core.wmem_default = 31457280

# Maximum Socket Send Buffer
net.core.wmem_max = 12582912

# Increase number of incoming connections
net.core.somaxconn = 4096

And I put these in limits.conf:

*         hard    nofile      500000
*         soft    nofile      500000
root      hard    nofile      500000
root      soft    nofile      500000