Well, my statement regarding the ease of this keyboard repair was apparently premature.
I am going to stay optomistic that it is just the ribbon cable at fault because this unit looks practically new and was very complete. If the issue is stress on the ribbon cable rather than damage to the membrane, I hope I can still make a repair. Otherwise, I don't think I have the fortitude to fix this thing. Onwards...
I flip the little TS1000 over to investigate opening it up only to find the warning "No user serviceable parts inside." We'll see about that... Peel the feet off, remove the 5 screws and look inside.
At first glance, I see what appears to be a ground strap that is not connected properly. It looks like a dry solder joint due to insufficient heat on the thick strap. This is almost certainly not the cause of our keyboard issues, but it will get fixed before the TS1000 is reassembled. 2 more screws to remove the circuit board and the problem is apparent.
I had thought that the ribbon cable was a separate set of wires that connected the membrane to the circuit board. However the damaged ribbon cable is part of the membrane keyboard. Fortunately, it broke right at the circuit board, leaving plenty of good ribbon cable.