I'm with Mike, I use the 9" long keyhole dogbones for the same reason.
I will use the "short ring" if the water is so rough that the waves are hitting me in the bum.

For a two-way keyhole system, you could make a ball rig that had a ball at each end with a tie point off-center between them.

Here is a page about a quick-release system. http://www.rwo-marine.com/newproducts/main.htm
I don't like the idea of using the quick-release and possibly losing the hook during a race.
Perhaps a pivoting hook release could work?

Also, the standard trapeze system has the line tied to the dogbone and then run through a block or a thimble and then tied to the bungee cord.
This causes the line to wear and get nicks.
I tie the tail end of the line to the handle and run the bungee through the block and tie it to the dogbone.
I haven't been dunked from a broken line since I started doing it this way.
Some of the Charlotte sailors even used wire rope, swedged on.