only outbound connections permitted

I'd ask for approval in writing from my boss to play this game. If received, you could perfectly well set up a $6 digital ocean box and ask sshd to listen to 443. Then...

   ssh -R 443:localhost:3000 -N my_remote-server

is a perfectly good outbound connection?

Obviously, you'll want some iptables on the remote end or for your local box not to have anything valuable on it, but it will let you test webhooks.

I run an sshd on 443 for this reason. Helped me bypass some corporate firewalls in the past, very useful when you go onsite.