Can I ask specifically what kind of dynamic stretching you were doing? I have chronically tight hips that leave me unable to perform "adequate" squats - poor range of motion and balance on the squats, and lack of power. I'd love any tips you have to offer.

Not much, actually. Swinging a leg at a time back and forward, and left and right, as well putting a foot at a time forward and doing a pike stretch down to that foot and right back up again, walk a couple of steps and doing the other foot (like #2 here, but a foot forward at a time: http://www.wikihow.com/Get-a-More-Flexible-Back).

Strict good-mornings are also quite good once you have decent amounts of flexibility. Strict = make sure your back stays arched, push your butt as far back as possible, with a slight bend in your knees, and hinge/bend at the hips. Essentially you should feel it in your thighs and butt and not elsewhere; if you start losing the arch in your back, you've pushed as far down as you can go, go back up and repeat. It's more important to keep form than forcing yourself as deep as possible - you'll get better depth soon enough.

I've later incorporated some static stretches including several of the one in the wikihow link above, but the ones above were enough to see dramatic improvement when done a for a few minutes a couple of times a day.

I also do asian squats regularly (so effectively sitting down in a squat position, unloaded, for as long as I an do - a few years back I wouldn't be able to get up without intense pain from that position, if I got into it in the first place...) and feel that helps me increase the depth I get into (and it's made it so much easier to play with my young son, to be able to effortlessly squat down to him instead of ruining my knees...).

That's good to hear, thanks. I have always had very good flexibility, so it was never an issue for me. I do stretch my hamstrings and IT band sometimes, and static stretching certainly has it's uses.

Glad to hear dynamic stretches worked for you!