Route traffic to specific sorry server path
yes, you would need to install the sites SSL certificates on your F5 to intercept/terminate/ansylse/offload the HTTPS communication (many names for the same approach). Without doing this, the F5 would not be able to to interact with your client on the HTTP protocol layer. This layer is required to perform HTTP redirects.
And yes, if the Sorry web server support lets say .htaccess or mod_rewrite you can teach the Sorry server to redirect or rewrite request for "/" (Root-Web) to the "/down" maintenance page. you would fix your issues on the server itself...