Wow, that is pretty bad.
Have you tried re-loading the firmware and/or reverting to an older version of firmware?
Mine reports 1.1.0-RC6 at the splash screen, for what it may be worth.
I routed my stepper wiring fairly far from the display cables, but don't have the cables shielded at all, nor are my stepper wires twisted to any extent or braided.
The only real issues of this sort for me have been a result of heavily used SD cards.
They do have a finite lifetime for writes, and for some brands that lifetime is shockingly short.
Oddly, I have experienced the same sort of issue when using them as music media.
I get skips, jumps or hangs in .mp3 file playbacks to the point where I have had to actually discard some cards.
This, I presume, is a result of memory cells not "remembering" properly.
Enough to be written and verified, but not stable enough longer term.
I am however seeing some indications of contact wear or contamination on my SD card socket lately.
It sometimes takes two firm insertions of the card for it to be recognized as present.
However once recognized I do not have trouble with them.
On the other hand, I have had problems when using the USB port, which is merely a phantom serial port to the computer.
Thanks to a suggestion from @heartless I set the baud rate to 115200.
I also set the receive buffer size in the printer firmware to 256 bytes rather than the default 128.
Prior to doing that it would exhibit the same sort of symptoms you describe for the SD card including randomly moving to one or the other of the home limits, skipped print segments, and stalling out completely.