I started off doing this with a bungee cord inside a piece of tubular nylon webbing. Like you I got a 2:1 extended to contracted ratio. That year in the Bahamas I talked to another boater who had used surgical rubber tubing inside a piece of polypropylene hollow core water ski rope. He had a better ratio than I did, so I set out to copy his setup. Before I got around to it, I ran across an Airhead Anchor Bungee and bought it. It has rubber bands inside its ski rope and gets a ratio of 3.5:1. I bought it and replaced the plated steel hardware with stainless. https://www.amazon.com/Airhead-AHAB...fd-8c96-d944a4360a5c&pd_rd_i=B00SMDQW3Q&psc=1 Others have what appears to be the same but cheaper. https://www.amazon.com/Greenfield-P...fd-8c96-d944a4360a5c&pd_rd_i=B003BM5LUI&psc=1To add a detail to the above post, it is 50' of 1/4" bungie cord placed inside 100' of polypropylene hollow braid: https://www.amazon.com/Hollow-Braid-Polypropylene-Rope-inch/dp/B01N81EG0R?th=1
The hollow braid protects the bungie. We use yellow color because it is easy for others to see that there is a stern line out. The 2:1 length is necessary to accommodate the bungie stretch.
The trick is in judging the distance correctly. The other day I dropped it a bit too far out coming into a dock and just as Michele was about to step off the dinghy we started slingshotting backward...
And yes, judging the distance from where the anchor bites to the beach is a challenge. I added a bit of rope to the dinghy end of it to compensate for my shortfalls.... or should that be long falls.