There's a major problem related to the Dec axis on the mount that effectively prevents it from being guided in the southern direction. This shows up in all the operations you performed with the system. During calibration, the Dec axis moved normally to the north but then never moved at all when the calibration tried to switch to south guiding in order to put the guide star back to its starting position. The backlash test you did with the Guiding Assistant makes the situation pretty clear:

The red data points show the mount response to 27 consecutive guide commands to the 'north'. The green data points show how the mount responded when the direction was reversed and another 27 consecutive guide commands were issued for south moves. As you can see, the mount didn't respond at all. Each pulse lasted for 0.5 seconds, so the total series of 27 guide commands south represented a total of 13.5 seconds with no movement. This is almost certainly a mechanical problem that you will need to fix. It could be due to a very large amount of "slop" in the Dec drive gears which should be easy to determine. It might also be caused by something else like a loose set screw or some other fixture/fastener in the drive system that has become loose. In either case, the mechanics needed to be corrected. That said, before you start tearing into the drive system, you should be absolutely sure that there isn't a cable routing problem of some kind that's interfering with the ability of the Dec axis to move smoothly and freely in both directions. You also need to be sure that the payload is well-balanced in Dec and the Dec axis clutch is tight. The Meade SCT is fairly heavy so if it isn't well-balanced in Dec, it can create these kinds of conditions. Also, be aware that successful slewing of the mount doesn't tell you anything useful about its ability to be guided because the amount of physical energy used for small guide commands is typically hundreds of times smaller than the energy used for slewing.
Good luck,
Bruce