Okay, so smartctl tells us that the drive definitely has media errors -- and so there is no need to blame the cables/connectors (yet).

If you have the patience to continue writing zeros until all of the errors are repaired, then go for it. But at this point I would pull the drive and send it in for a warranty replacement.

Or at least install it in a PC and run a Seagate low-level format on it. That is, assuming that Seagate provides software (web site?) to do this, like other manufacturers.

Cheers