I found a site on the Internet that has circuit boards for hard drives and saw that he even had my exact Seagate Barracuda 7200.8 300 GB SATA model. $50 was a little steep, but hey, it might actually work...
http://hdd-parts.com...-7200-8-sata.html
Installation was trivial. 6 each T8 Torx screws and lift off the board. Contact is made through 2 arrays of spring-loaded contacts underneath. Install the new board. Hook up an external SATA to USB adapter and fire it up. No smoke or fire this time. :-)
The drive spins, and there's some servo noise, but there was never unambiguous indication of the head moving. Winders doesn't see it and there's no indication that the USB controller sees anything either. :-(
I'll mess around with it some more, but it looks like a real possibility that the data's really gone.
Cheers,
Scott.
(Who wonders if this technique would be a solution for the bricked 1.5 TB Seagate drives.)