Sorry for the lack of updates. I suffered a particularly gruesome injury to my finger this past weekend while working on another project. Nothing a little super glue and duct tape couldn't fix.
I fixed the loose ground strap tonight. I used a soldering attachment for a propane torch which worked perfectly. My little soldering iron was not going to get hot enough to heat everything up. The TS1000 is much more stable with the strap secured, but I still don't have audio output during a SAVE command.
The three jacks on the TS1000 are identical 3.5 mm phone connectors. It seems possible that a previous owner connected the 9v power cord to the MIC jack, frying some component. I will do some research and testing tonight to try and track down the problem.