Paul,
This is probably software-related. You may have a bad hard disk driver, or something may be wrong with the system software.
Try to start the SE from a Disk Tools floppy, holding down the four keys Command (Apple) + Option (Alt) + Shift + Delete (Backspace). If possible, update the hard disk driver (Update in Apple HD SC Setup). If necessary, reformat the hard disk (using Apple HD SC Setup or a suitable third-party utility) and install a fresh system. Reformat the hard disk when it is in the SE. Install the new system directly at the SE.
Have you tried the British System 7.0 (and its Disk Tools floppy)? With access to the 4400/200, you should not have a problem creating a full set of sector-copied System 7.0 (800K) floppies from disk images (via Disk Copy 4.2).
Jan