The problem with sending the to Bay Ridge is you wind up having to deadhead trains from CI Yard to Bay Ridge somehow, which would both waste time and disrupt service. Perhaps a permanent terminal of Kings Hwy or 86th-Gravesend on Sea Beach would work, though that could be a messy merge after 59th...
Alternatively, you could send it down West End, but Sea Beach needs the extra service more (based on ridership), and since trains are run with crews, I'm sure logistically running it down Sea Beach makes more sense. Also 45th and 53rd are high ridership stations that could use some extra service (especially when 53rd re-opens).