You have a fair lead from an existing cleat to a bow chock. I have an anchor (Danforth plow) on a roller, but no centerline cleat. When I drop anchor I run a snubber line from the rode (all chain of course) through a bow chock to one of the 12" cleats I have on either side of the windlass.

As far as getting the rode out of the anchor locker, it seems to me that a small slot cut in the locker door would work adequately. That way the rode can stay attached to the anchor. I assume, of course, that there is a drain in the anchor locker that lead overboard and not into the bilge so that rain isn't a problem