Speaking of out of the saddle, I find the further forward and more erect I can stand, the easier it gets.

When I do this, the visualization of bringing the knees to the handle bar becomes even more important.

Nowadays, I find that I PULL myself uphill much more easily than I MASH myself uphill.

The more erect and forward-leaning stance lets me use my the big thigh muscle that runs from the pelvis to the knee cap to flex my hip, or bring my knee up to the handlebar.

The forward-leaning part lets me pull earlier in the spin.

I no longer feel myself pulling up on the handlebars while pedaling uphill out of the saddle.

In fact, now that I have a more circular spin, I no longer feel myself using the handlebars for anything other than hanging on to the bike.

If a rider finds himself pulling up on the handlebars in order to mash harder on the pedals, he works much harder, with less efficiency, than he needs.
And, eventually, his knees will punish him for abusing them this way.

When we mash and pull on the handlebars, the quads in the fronts of our thighs not only straighten our leg, as if doing a dead lift with a weight in our hands, they also pull the shin bone up into the knee joint and needlessly multiply the forces meeting in our knees.

If the rider pulls himself up the hill, he will still mash, whether he wants to or not (otherwise he would fall down or collapse on his bike), but he will also greatly reduce the stress on his knees; and, although it will feel like he does most of the work with pulling, he will have actually balanced the amount of work done by the fronts of his thighs with the amount of work done by his trunk, buttock and hamstring muscles.
The quads in the front of the thigh will feel as if they do less of the work, but, finally, they will really do only do the same amount of work as the rest of the body, as opposed to doiing the majority of the work.

On a long hill, the rectus femoris will begin to complain in a way not felt before.
This comes from the rectus femoris flexing the hip instead only extending the knee.

I saw a picture of a Jan Ullrich, as he rode uphill out of the saddle.
As he brought his knee up to the handlebar, the rectus femoris muscle in his thigh stood out like a python.
It stood out like a python because the other three muscles of the quadriceps remained in a relatively relaxed state as the hip and the knee flexed (as the hip and knee bent, as opposed to straightened).
As soon as Jan would have begun to mash, the other three muscles in the quadriceps would have reburied the rectus femoris as the knee extended.
However, for that portion of the spin, as Jan flexed his hip and brought his knee up to the handlebar, this impossibly huge single muscle in the front of his thigh stood out like a live snake.

Almost the single largest gain from rising out of the saddle comes from making it possible for this major thigh muscle to flex the hip (raise the knee) instead of straightening the knee.
It won't, can't work if we already have our hip flexed (body bent forward) because of our position in the saddle with our hands on the bars.
We need to straighten out our body for this mega-muscle to do its knee-raising job.

For that reason, I ride with bullhorns so that I can lay out over the handlebars in a climb.
I lean waaaay forward and climb better than anything else I do on a bike.
As soon as my cadence falls to certain point, I pop out of the saddle and change my body's organization so my front thigh muscle can help pull the rising pedal up.