Put one length of line between the two D rings. Use an anchor bend to attach it to each D ring. Then put a butterfly knot (loop) in the middle.
Attach a painter to the butterfly knot with a double sheetbend. This should be a permanent set up, or at least something that you set up each time you launch the boat, regardless of whether you intend to anchor.
Then you drop the anchor and allow plenty of line out. If you have enough line out, it will hang in a curve and take up the shock without the need for a bungee.
Make a bight in the anchor line and attach the painter to it using a double sheetbend. (A single will do if you are not leaving the boat unattended.)
Then keep the loose end of the anchor line on board, with no tension on it.
The tension will then go anchor>chain>anchor line>painter>loop between the two D rings.
Why use carabiners when knots are free, and you need a knot to tie the carabiner on anyway?
Rope Knots - Best Knots Animated and Illustrated