Ok, guys, lots more stropping practice! A few more thoughts as well...
I tried stropping with a piece of paper folded to 1 inch in width, to get my pressure right. Then I tried it with the blade. My X-pattern is getting much better, and I'm starting to hear the right sound probably 80% of the time.
I will admit I have some unique challenges with this. I think a lot of the reason I started out pressing so hard, even though I'd read so many times not to, is that I have dicky wrists. I hurt them pretty badly several years ago, and I frequently find myself having to use more force than most people do to do the same tasks. I'm used to having to compensate for having weak wrists.
Well, as soon as I stopped trying to compensate, the blade was laying flatter, the sounds were getting better, and I had a lot more control. I found my fingers backing further away from the blade (where as before I'd been grabbing it right under the heel, now my fingers have backed off to the top of the scales, only keeping the blade straight by keeping the tang in the scales), and I'm finding I am having an easier time adjusting my movements.
Still, despite my efforts, not much improvement. I'm gunna ship her off to Onimaru55 on Monday and when she gets back, I'll know how to treat her this time...
Thanks to everyone who helped out! Hope some newbie reads this and doesn't make the same mistakes...