Hope this makes sense:
I was riding today along the LA river. This is basically two dikes lined with concrete, and at each street bridge the path dips down and comes up again on the other side. So it is a long steady effort punctuated by sharp efforts to keep up momentum.

I was feeling sort of tired and my speed was gradually dropping. But rather than stalling out on the underpasses, I easily powered up the other side and ended up going faster on the exit. OK, I asked myself, what am I doing different here? I wasn't standing, or shifting position, just laying down a whole lot of power easily.

Finally it occurred to me: I was powering from the hips. Not like my hips were moving noticeably, either on the flats or when powering up a rise, but maybe my new saddle and bibs were freeing things up a bit. Somehow this seemed to bypass the tired muscles and kick in fresh ones. So I continued this subtle change on the flat, and suddenly I was flying along on fresh legs.

I have noticed this effect after exiting a crowded path and opening it up on the road. Or doing a short fast ride instead of endurance mode. It feels easier, even though the watts are way higher. I wonder if this comes back to using core strength, and giving the large muscles a firm base to act against.

Either way, it will be my focus of training for a while, trying to make this my normal pedaling mode.

Could be. My first thought is the glutes which are part of the "core".

I'd be curious to see what your results are after trying it a while. There's 2 things I know of:

1. On the one hand, you can get decently increased power and endurance if you can get everything in your body to align better. So like rather than just using your quads pedalling, if everything lines up you can get quads, glutes, and core all working together.

2. On the other hand, when people run into this (including myself), we often find that the new way to pedal has a lot less endurance than the old way. Probably you were using more quads before, your quads got warn out, you shifted to using glutes which were still fairly fresh. But it doesn't last - your glutes also get worn out and a lot faster than your quads.

Could be either, I'd be curious to see how it goes.

Sounds about right. I know that when I'm using my hips, I can ride 1-2 mph faster, for as long as the muscles last. The more often I do it, the longer I can make them last; but then I move to one of my other bikes and I have to start all over again. It seems minor differences in position make for major differences in how the muscles are coordinated.

Sort of like the story of "The Little Engine That Could" "I think I can...I think I can. I know I can... I know I can."

I have been "Driving from the hips" on my daily commutes, 6 mi each way. Trying to do it at all times. My average speed is up almost 2mph, crusing speed 2-4 mph. So no question it is effective, but also get very winded. It is hard to do it at a more moderate effort. My glutes are starting to feel it, but my back feels fine. I think I can train to both sustain in longer, and do it more moderately.

I think this technique has only occurred to me now, after some 200,000 miles because of some recent changes. The biggest is changing to a crank length proportional to my leg length: 37" inseam, 200mm cranks, has simply made everything better. With my old standard, 180mm, it really limited the effort to my quads. You might say, I wasn't making use of my best ASSets.

""Finally it occurred to me: I was powering from the hips. Not like my hips were moving noticeably, either on the flats or when powering up a rise, but maybe my new saddle and bibs were freeing things up a bit. Somehow this seemed to bypass the tired muscles and kick in fresh ones. So I continued this subtle change on the flat, and suddenly I was flying along on fresh legs.""

And then you woke up

is that where they had the chase seen in terminator 2, when both terminators were chasing the kid on the dirt bike?

Sounds like the caffeine kicked in.