A horizontal windlass with a short fall under is trouble. Been there done that, the chain piles up and then jams the windlass.
Maybe a vertical would work
mounted behind the chain locker on deck
? The chain goes around the windlass and falls into the locker ...open doors?
The other possibility is make your chain locker deeper... there must be more depth
under it up there in the bow.
On the boat
in my avatar, I made a sturdy vertical windlass mount that was bolted inside the chain locker to the aft bulkhead and floor. I cut the locker doors to fit around the protruding windlass.