Irule Vs rewrite - FQDN hostname

You don't need to specify https nor the port on the host header, cause those are specified elsewhere, https is by using a ssl servers profile and the port is at the pool member.

Alsop testing if uri starts with / is useless since all uris stars with /. 

If I understand correctly your requirement, why not first redirecting user to target path, then doing just the host replacement. 

Something like this that :

when HTTP_REQUEST {
if { [HTTP::uri] equals "/"}
 {
    HTTP::redirect "https://[HTTP::host]/your/full/path/something.html"
 }
else {
     HTTP::header replace Host ServerName.Domain.com
  } 
}