There is nothing currently built into the product to achieve this. Other customers have posted similar requests on the ideas forum:
One major issue with relying on the Tableau Server to redirect to a static "server maintenance" page was mentioned in your post - what if the Apache component itself is down? Then obviously it can't redirect any traffic.
One approach would be to configure a load balancer or another web server to act as a proxy in front of the Tableau Server. Then, if requests sent to the Tableau Server fail, your load balancer/proxy can begin routing requests to a static "Server Maintenance" page until the issue can be resolved.