Rather than fighting to understand webhooks from the various git-hosting services I've decided that volume is low enough that I should just host the git repositories myself.
I've spend a few evenings preparing for this transition, updating documentation, and reworking my codebase to avoid all use of webhooks.
It's a fun update, which will simplify the service for new users, but keeping both systems in use at the same time makes it a little more complex than I'd like. I guess I need a flag-day in a few months where I drop the old webhook support.