It's too early to tell if this will be a "thing that works". but I'm impressed with early indications.
Friend Dave C forwarded this Kickstarter link about these Infinity Pedals:
Below, find a video about how they work:
They look like the engagement would be easy to hit through 360° of rotation, and the shoe cleat looks like it will fit in a standard Shimano SPD sole channel. They're light. And you can get a pair for $149 on the Kickstarter, which means the selling price, if they get offered, will probably be lower.
There's not a road bike version, but light SPD shoes are available. And they certainly look like they would clear mud and sand better than Speedplay pedals (two of my riding companions who use Speedplays travel with toothbrushes to clean out the gunk on gritty or muddy rides).
I'm impressed. I haven't supported the Kickstarter yet, but I might.