This is how we used to retrieve the anchor and chain on my fishing vessel. Regularly used to anchor in 120 metres of water in a fresh current similar to what's happening in the video. 18 tons of boat driving forward and the buoy often used to disappear a long way down before the anchor would pop.

We used a similar unit to these.
http://www.ebay.com.au/itm/STAINLESS-STEEL-ANCHOR-RETRIEVER-ASSIST-RETRIEVAL-DEVICE-SYSTEM-RING-SNAP-HOOK-/360879227174?hash=item5406140126:m:mbL1g9H5YivAet_HphLMPyA

The anchor would end up hanging in the ring with the chain under it. Just drift down or motor down the anchor rope to retrieve.