Old external HDD drive not recognized properly in new enclosure I've tried searching Google, the Apple Forums, and here for solutions to this and none of them seem to address the issue.

Have been using a Seagate 3TB external HDD for years as a Mac formatted external library and also a partition for TimeMachine, a STBV3000100.  The main problem seems to be that the Micro-B connection on the control board in the enclosure is not very sturdy and I have had to keep the cable at angle to maintain connection.  This is very far below optimal and worried it could lead to damaging the drive.

Bought USB SATA dock (powered externally and can handle 3TB, already checked that, and have used it for other drives since then and it reads the others fine as they were in their other enclosures) and received a "the disk you inserted was not readable by this computer" dialog box with the option to initialize, ignore and eject.  I figured maybe it was a problem with the dock so I bought a full enclosure.

Installed in new enclosure (non-Seagate, but rated for 3TB and beyond and external power) and having the same issue.  If I get the controller from the original Seagate enclosure that I bought the drive in and manage to get the Micro-B to work at JUST the right angle to read the drive then it registers as the normal drive and sees everything, including the TimeMachine partition, properly.

What can I do to resolve this?  And what about the control board from that enclosure (or whatever is causing the issue) is causing my Mac to recognize it when it's connected to that but nothing else?

The screenshots below are from when I've plugged it in with the new enclosure, but the same errors appear when I used the dock.  

A few notes:
- It doesn't even give me the option to 'Verify Disk' or 'Repair Disk' which similar (but not the same) issues seem to be resolved by
- I don't have another way to access this data (external and TimeMachine) so simply formattting without transfering it first isn't an option, I neeed some way to access it to copy it to a new drive at least first if that's the only way.
- Running OS X 10.8.5 and this is the only computer I've used this drive on.
Answer from bwDraco on SuperUser
This version posted as Community Wiki


  The enclosure exposes the drive to the computer as an Advanced Format 4Kn device, allowing the use of MBR for compatibility with
  
  Windows XP systems. When the drive is removed from the enclosure, the
  change in logical sector format results in an invalid partition table.
  
  
  External hard drives larger than 2 TiB in capacity often expose 4K sectors directly to the operating system. The 2 TiB limit commonly
  associated with MBR is tied to the traditional 512-byte sector size;
  4K sectors are eight times as large and therefore extend the MBR limit
  to 16 TiB. This allows the use of MBR on disks larger than 2 TiB in
  capacity, enabling use on Windows XP and other systems which do not
  support GPT.
  The underlying hard drive uses 512-byte sector emulation for compatibility with legacy systems. This means that while the disk
  physically has 4K sectors, the immediate host device (in this case,
  the enclosure) sees 512-byte sectors. However, to perform the
  aforementioned MBR expansion and enable Windows XP compatibility, the
  enclosure makes the drive appear to the computer as having 4K native
  sectors.
  When the drive is removed from the enclosure, the 512-byte logical sectors of the underlying 512e disk are exposed. This results in an
  invalid partition table that cannot be correctly interpreted. The
  746.52 GiB value you gave for the last "partition" when the drive is connected directly is precisely the amount of space that lies beyond
  the 2 TiB limit for MBR drives with 512-byte sectors.
  
  
  More details about the implications of this conversion are available
  in this blog post.