This project doesn’t sound like a good fit for https://build.snapcraft.io. Instead, I’d suggest using Launchpad directly.
Once you have a snap build set up in Launchpad, you can then create a Git hook to trigger builds using lp-build-snap (snap install lp-build-snap):
$ lp-build-snap -h
usage: lp-build-snap [-h] [--lpname LPNAME] [--arch ARCH] [--series SERIES]
snap_name
Trigger a Snap build in Launchpad
positional arguments:
snap_name Name of the Snap package being built
optional arguments:
-h, --help show this help message and exit
--lpname LPNAME Launchpad user or team to build from (default: ev)
--arch ARCH Build architecture to target (default: amd64)
--series SERIES Ubuntu release to build against (default: xenial)