aicabsolut "--feel like I need more resistance from the gears. I figure it'd be easier to learn in a climb when I need to rev up my speed a little bit as my legs start to burn."

there's a couple ways to get that higher gear.

One is what some call "the magic gear". On a climb where you "run out of gears", you're in the granniest of granny gears and wish there was a lower one pop it 1-2 gears higher (folks somewhere here we have a thread on shifting under load and sometimes .... you just can't do that! but if you can...) climb standing till you've got a little rest then voila!! shift down 1-2.

It's magic, lower gears!

Or...let the bike come to you. If you need some resistance to climb standing feather the pedals and let it slow down a little till ... voila! You can stand.

Don't know if this is right.

"I get the concept of rocking the bike, but I'm worried about the sideways topple."

The feeling I try for is not rocking the bike but relaxe the hands and you kinda toss it back and forth lightly like tossing a light bean bag from hand to hand. Don't know if that makes sense. It's hard to keep the upper body relaxed.

Hope this helps.