On Apache, the anchor, chain and rope for the usual depth I anchor in live in a builders bucket in up in the anchor well in the cuddy. When we're ready to anchor the bucket comes out and the anchor gets thrown over the side once the buoy and ring is clipped on.
Recovery is the same but in reverse. The buoy, with anchor and chain suspended below gets pulled by hand alongside (not hard work as the buoy is holding the anchor and you're only pulling it towards the boat). Once alongside the rope, chain and anchor is wound back into the bucket, then re-stowed up front.
I'd consider going back to the Alderney method on Jersey Girl as its quicker and safer than using the windlass because I wouldn't need to go up front with no railings in a swell to sort out any tangles in the gypsy.