$ sudo mdadm --assemble --auto=yes /dev/md0 /dev/hde1 /dev/hdf1 /dev/hdg1 /dev/hdh1

Did this, and it says:

mdadm: device 3 in /dev/md0 has wrong state in superbock, but /dev/hdh1 seems ok
mdadm: failed to RUN_ARRAY /dev/md0: Input/output error
$ sudo mdadm --assemble --auto=yes /dev/md0 /dev/hde1 /dev/hdf1 /dev/hdh1 missing

mdadm: device /dev/md0 already active - cannot assemble it

$ sudo mkdir /mnt/md0
$sudo mount /dev/md0 /mnt/md0

mount: you must specify the filesystem type

$ sudo mount /dev/md0 /mnt/md0 -a

mount: you must specify the filesystem type

$ sudo mount /dev/md0 /mnt/md0 -a -t jfs

mount: wrong fs type, bad option, bad superblock on /dev/md0, missing codepage or other error (could this be the IDE device where you in fact use ide-scsi so that sr0 or sda or so is needed?) In some cases useful info is found in syslog - try dmesg | tail or so

$ dmesg | tail

--- rd:4 wd:3
disk 1, o:1, dev:hdf1
disk 2, o:1, dev:hdg1
disk 3, o:1, dev:hdh1
raid5: failed to run raid set md0
md: pers->run() failed...
EFS: 1.0a - http://aeschi.ch.eu.org/efs
EFS: cannot read volume header
EFS: cannot read volume header
JFS: nTxBlock = 7945, nTxLock - 63562

...so then I tried restarting it and doing the "missing" without doing the other stuff first; no dice. Then I tried assembling the array calling other disks "missing" and it still doesn't like "device 3" regardless of the order I type it in.

When I tried to build it from F, G, H and E (in that order) it said "device 3 has wrong state but /hdh1 seems ok" as usual; next:

$ dmesg | tail
raid5: device hdh1 operational as raid disk 3
raid5: device hdg1 operational as raid disk 2
raid5: cannot start dirty degraded array for md0
RAID5 conf printout:
--- rd:4 wd:3
disk 1, o:1, dev:hdf1
disk 2, o:1, dev:hdg1
disk 3, o:1, dev:hdh1
raid5: failed to run raid set md0
md: pers->run() failed...

just for giggles, I tried mounting it as jfs, hfs, and ntfs. At least I got a different error out of ntfs ("the device /dev/md0 doesn't have a valid NTFS. Maybe you selected the wrong device? Or the whole disk instead of a partition? Or the other way around?")

And that's about as far as I can get. Unfortunately I suddenly got a job down in LA so I'm getting on a plane in ten hours. I'll have this lovely little disaster to play with again in about a week... and yet again, I welcome any and all advice.