Double-sided SPD or SPD clones with SIDI Dominator shoes. Yes, they cost real money, but they last forever. I've had my SIDIs since '97 and the interiors still don't show wear. Easy to walk in, quick to clip in, very efficient. For hiking, you'll have to carry a second pair of shoes, but you should be able to do that and still stay close to 20 lbs.

While it's true that riders don't normally pull up on the backstroke, we do sometimes, and sometimes pull up hard. Most efficient riders unweight the pedal on the backstroke. But mostly the difference with toe clips or clipless is that you can push forward at the top of the stroke and pull back at the bottom. It was a revelation when I got my first bike with toe clips in '63. I was turbine-powered! Clipless is even better and doesn't cut off the circulation in your feet. Much warmer and more comfortable.