Continued vibration with the clutch disengaged would tend to rule out any transmission/driveline issues, so that points back to engine mounts as a likely culprit.

Surface rust on the flywheel would explain the abrupt clutch engagement due to the rougher surface, but that should smooth out as the rust gets buffed away by the clutch friction disc.

U-joints with grease zerks typically put the zerk (or a fitting where a zerk could be screwed in) at the crux in between two arms, but sometimes they're on the end of one of the bearing caps, or of course some don't have grease fittings at all.