We've just deployed an enhancement to 3rd party notifications in DeployHQ, not only with the ability to now select if they're sent on failed or successful deployments, but also when the deployment starts.
When configuring a 3rd party notification, such as Slack in your project, you'll now find 3 toggles that can be individually set.
These options will also be available in your project templates, so that you can set up notifications only on deployment start for example, then apply that to all new projects in your account.