I actually ended up using one of these: X10 Chime and plugging it into a zwave outlet I don’t otherwise use. Then setting the outlet to turn on when certain contacts are opened. It’s not a great workaround, since you have to have an app that turns the outlet off again. But atleast it’s very little delay.
If you have an old tablet laying around you could install the client and have it chime (or text to speech) the push notifications. That is what I did with an old nexus 7.