Just needed some opinions/suggestions about my current scenario.

A blatant disregard for stealth using nmap, results in "all 1000 ports filtered". Hpinging them with packet capture results in Acknowledgement from many ports...apart from 80 none of them well known ports. Now when i scan just 80 with nmap, it comes filtered. Obviously some sort of IDS or Firewall singling out nmap packets.

I tried banner grabbing, nothing concrete. Any suggestions of where to go from here.

This is a general question regarding enumeration of perimeter device (router / firewall). If certain ports are open on those devices leading to one or more hosts, incase of scanning and fingerprinting the response would be from the end host hence enumerating the host.
What would be the ideal way to enumerate and fingerprint the perimeter device?