Would it be possible to allow a check failure to first notify one of the contact groups in my organization before it notifies the Linode team? The way I'm thinking of using the managed service as a fallback for my ops team. If a check fails, notify my ops team and if nobody responds in a reasonable time (say 5 minutes but perhaps this could be configurable based on our internal SLA for the service) then the Linode team takes over and makes the fix instead.

I don't really have a dedicated ops team but a few of my developers have the ability to access the boxes and can make changes to the puppet configs. I would prefer that as a first line of defense and Linode as the fallback.

Is that reasonable or am I missing the point?

Linode Managed was designed to notify Linode staff first and foremost, and it is our responsibility to notify your contacts as part of our response to the issue. You could certainly just request that we notify your team of the issue instead of us responding by fixing, but there isn't a system in place for us to start normal procedures after a period of time has passed without response.