Okay, I finally figured everything out. I spent a lot of time in the command prompt failing before I finally succeeded.

The primary problem is that "system partition" (as Microsoft calls it). That's where MS decided it should put all the boot information for Windows 7. Most cloning tools I've seen don't clone over two partitions at once, so unless you can do the whole disc (which I couldn't since the SSD was smaller), you have to figure out a way to clone Windows over to the new disc without that boot partition.

The answer is to basically wing it I cloned the partition that contained all the actual files for the OS. Then I used bootrec and diskpart to recreate the MBR data. I also had to run startup repair at least three times until it wouldn't work anymore. I think I'm also forgetting another command or two, like bootsect. I pretty much ran everything.

But that still left me with this autochk error message that prevented Windows from booting. Everything looked good, but the OS still wouldn't boot! Grr.

The solution, as elaborated by the second answer here, was to load the registry hive from the drive (instead of from the recover console), and change the signature for the system drive in the disk's registry to the signature for the system drive in the recovery console. Once I did that, unloaded the hive, and rebooted BAM! I was up and running in Windows! Woohoo!

It was a serious PITA, but even though I've only been using this SSD for a few minutes I'm already blown away. I timed my startup from before the upgrade, and I've gone from a total of SIX minutes (including POST), to somewhere around 90 seconds. Most of that time is spent at POST and also, for some reason, in finding my keyboard and mouse at the Windows login. I have to wait for at least 20 seconds for the peripherals to get recognized before I can enter my password. That means that the whole operating system is loading in around 30 seconds, including at least 20 system tray icons-worth of background programs.