Thank you all for the thoughtful responses, this is very helpful.
Zanshin, I had not thought of diving on the chain to attach the line at a lower point, that is an interesting thought. Maybe you could even attach to the anchor and pull it up first ? and bring the chain up after it. Or attach a line to the anchor with a float before you even set it so that you could use the line later to pull the anchor up if you needed to, but then somebody might pull on the line and unset your anchor.
Hmm, I wonder if you could attach a float to the anchor that was just enough to float the line but not unset your anchor, then lead the line back to the boat, then you could pull the float under the water so that nobody could grab it, and only release it so that the float came to the surface if you needed to pull the anchor up using the line.
svHyLyte, that seems like a good solution, using two winches instead of one, it seems like it would save you from having to tie off the chain you have already brought on deck while you move your line back up to the bow.
Pending on the type winch you have, you may be able to use a 1/2" battery powered drill with a socket as a backup power source.
Using tackle, a two fold or double luff, attached up the mast aways to lift said chain & anchor. Snubbing off the chain as you go for another bight of it. Landing the chain on the fore peak only on top of an old sail or sailbags, or fair leading down into the chail locker as you slack off on the tackle.
Boasun, thank you so much for answering. I am curious, does it matter how high on the mast you attach the tackle, I mean, is there more mechanical advantage to it if it is higher on the mast because of the angles involved ? Also, how would you move the line to take another bight of the chain, meaning how would you keep the chain from slipping back into the water as you moved the line to get another bight ? Thank you for using the right terminology, I am still learning and it helps me learn when I read it.