No experience with the 4096 specifically but I have repaired a handful of Seagate drives of similar vintage with
a) bad motor driver transistor
b) bad power filter caps
c) physically damaged components (e.g. inductor at the front edge of the top pcb on the 4026/4038 is quite frequently broken off)
Drop a note to David Gesswein at pdp8online. He developed the mfm 'emu' device which can read data off MFM drives in addition to emulating them. Even if the device isn't useful to you for this application he has a lot of experience with this sort of recovery.
Thanks for the replies so far, I am using David's reader, in fact he kindly added Sage / Stride-format support to it. Which I verified with the other 2 Stride-disks I have.
The issue is that ST4096 doesn't come online, headlock disengages, head seeks, but then goes offline. I have to assume it cannot locate track 0.