I got a replacement drive for rutabaga and got RE to do the actual driving on the array rebuild. It actually *was* trivial. Here's what we did:
1) run "hdparm -i /dev/sde" which will provide details on the device sde. We need the serial numbers for each drive, so do that for each drive.
2) Compare the serials to the drives in the machine. The one you don't have a serial for is the dead drive - it doesn't show up when you look at /dev and hdparm can't read it to get a serial.
3) pull the dead drive and replace with a new one
4) boot the machine and dump a partition table from a good drive to the new one like this: sfdisk -d /dev/sdb | sfdisk /dev/sdc. This gives us identically sized partitions to work with.
5) add the new disk to the array like this: mdadm /dev/md0 -a /dev/sdc1
6) check progress on the rebuild like this: cat /proc/mdstat

I've downloaded the seagate tools app (seatools_cli.tar) and I'll run it on the dead drive per Seagate's instructions when I get back. Once done it provides a number that I quote when I RMA the drive. My understanding is that I need to do this in order to ensure a successful RMA.