I'd like to make a report that Geekmaster's tool worked for me! My formerly dead Kindle is now in Diags mode!! Here's an account of the nature of my bricking (probably due only to the 3rd partition filling up):
I followed Geekmaster's instructions, and found it to be very straightforward. The only discrepancy on my particular system (which is Windows XP SP3) is that when I booted the Kindle into recovery mode it did not pop up a message identifying it as new hardware. So I went and found it in the Device Manager (under Human Interface Devices -> USB Human Interface Device) and found that it already had a driver associated with it, apparently from Microsoft. I tried to replace it with the driver in the Mfgtools directory, imxusb.inf, but got the message "Specified location doesn't include information about your hardware". Luckily Mfgtools worked anyway (after one attempt failed because I was overly hasty and it was in low battery mode - so for anyone as silly as me, make sure it's charged first).
I don't want to start pressing menu options in Diags mode that I don't have a good idea what they do, so I need a little more advice to fully unbrick: can I erase the partition from here, or do I need to boot into fastboot (after doing a little reading about how that works)? But from Diags mode I was able to mount my /mnt/us (with the menu option "USB device mode"), letting me back up my /Documents folder, including notes I'd taken on books, which I was afraid I'd lost forever. So already life is better. Thanks Geekmaster!