As a long time caver who did VERY long rappells, I learned to deal with
rope. DO NOT TRY to make a neat pile. I found the same methods apply
whenever I anchor.
When putting the line back in the locker, let it go in in a loose pile,
forget being neat but make sure the anchor is on top of the pile and
its flukes do not hook a loop.
When using the anchor, pull it out and set it on deck followed by its
chain and then by enough rope to anchor all put in a loose pile where
no loops hook the anchor. Cleat the rope. Then, reverse your pile on
the other side of the bow till you get to the chain. Now you know you
have no knots and you can put the anchor in the water with just enough
rope hooked around a cleat to slow your drift till you hit where you
cleated it before.

When pulling anchor. Pull it in and set it in a loose pile behind you
till you get the anchor in. Then make a pile on the other side of the
bow with teh anchor on bottom (watch the flukes). Then start dropping
coils into the locker, dont try to be neat or you will tangle it.
Finally put the anchor on top without hooking a fluke.

Yes, it seems like a lot of making coils but because it doesnt tangle
this way it is really fast. I have done this with 1200' of rope
without any problem.
However, one time someone tried to be really neat about a 600' rope and
I had to sit for an hour in a damned cold waterfall untangling rope.
Often cavers will carry rope simply by grabbing a handful and stuffing
it into a pack, followed by another handful, it never tangles that way.