Okay, I followed tuskenraider's advice, and it worked perfectly. Just wanted to follow up here with some details, which someone might find helpful in the future.
noegruts, thanks for the DriveImage XML suggestion. I installed it, but only had limited success getting it to correctly image my sytem drive. It's nice software for its price,
but it definitely still contains some careless/buggy code. (E.g., I was not once able to get a successful "Drive to Drive" copy. And right after the message telling me that it had failed, a second pop-up proclaimed success.
)
I was getting ready to pay for better imaging software (Norton Ghost or Acronis TrueImage) when I stumbled upon a free drive cloning tool from Seagate. It turns out that it's really just a rebranded (and maybe pared-down) version of Acronis TrueImage, which Seagate makes available for free if you own a Seagate drive. (Luckily(?), my drives are Seagate Barracudas.)
Seagate DiscWizard worked wonderfully. (Props to Acronis.) Steps I took, for the curious:
0) Enabled Intel RAID in the BIOS, to ensure that ICH9R drivers were loaded.
1) Cloned my JMicron RAID-1 drive onto another, single non-RAID disk. (DiscWizard made this easy.)
2) Tested bootability of the new single drive. Confirmed that boot into OS worked.
3) Disconnected the pair of drives from JMicron SATA mobo headers, and reconnected them to Intel SATA headers. Added them to a new Intel RAID-1 array.
NOTE 1: This was The Point of No Return for me; by creating the new Intel RAID array, I was losing the existing data on those drives. If I'd had more drives in hand, I could have mitigated this by using new drives in the Intel array instead of my old JMicron pair. (Just one spare drive would've been sufficient, since if everything went sour, I could have always rebuilt the JMicron array from one of its old drives.)
NOTE 2: I had to connect my single, newly created clone drive to an *Intel* SATA header, and NOT to the *JMicron* SATA header. I tried JMicron first, but DiscWizard failed to recognize that the Intel RAID disk was a Seagate disk. (And DiscWizard only runs if there's a Seagate disk on the system.) Had to shut down and connect the single drive to an Intel header instead of JMicron. Alternatively, DiscWizard, upon finding no Seagate drives, offered me the option to purchase Acronis at a discounted rate. How generous of them.
4) Used DiscWizard to clone the single disk to the new Intel RAID array.
5) Crossed fingers and booted from the newly cloned Intel RAID array. Success!
Thanks to all who helped. Your advice was invaluable in helping me to think through the problem.
FINAL NOTE 1: Some disheartening news: While formatting a large partition on the new Intel RAID-1 array, Intel's MSM console reported that one of the disks in my array had failed! WTF? Unlikely. I think that the drives were just too busy, and they didn't respond to the RAID controller fast enough, causing it to freak out. I rebuilt the array, and 5 hours later things were back to normal. But I'm a little nervous about how temperamental and precarious the array seemed. I should also point out that I'm using 7200.11 ST3500320AS, and not the ES.2 ST3500320NS which might be geared more for RAID use. Not sure, after reading reviews on Newegg, which would actually be a better/safer choice.
FINAL NOTE 2: FYI, it turns out that each disk of my JMicron RAID-1 array was usable as a plain ol' non-RAID disk without any modification. I had always wondered whether this was true--whether I could pop a RAID-1 disk out of its array and have it be recognized by a non-RAID controller. Maybe this is implementation dependent, but at least it does work with the JMicron JMB36X.