Just wanted to update all of you on this issue. I took the car in and they assured me that replacing the radio (JBL head unit) would take care of the problem. An hour later, I'm told that replacing the radio didn't fix the problem, but that the replacement radio worked fine (tested in another vehicle) until they put it in my car. The tech working on my car was completely baffled and couldn't figure out the problem, no record in the Toyota service database of this problem either. This was a Thursday night, and Toyota tech support was evidently closed for the evening, so they called first thing Friday morning, and finally got a response Tuesday morning. Tech support said there is a spring in the trunk that is arcing/causing interference with the wires and the amplifier (?!?) so I was to bring it back in and it would be a ten-minute fix. Toyota tech told my service department that would take care of it, and that they've gotten several complaints about this recently, but adjusting the spring fixes everything.
So, this past Friday, I had the car there at 7:30am, ready for my ten-minute fix. My father came along with me, as we were going to run some errands afterwards. TWO-AND-A-HALF HOURS LATER...after my father (who worked for 30 years in automotive QI, including working w/ Toyota) went out and gave the service department hell, we had an answer. In my case, the spring in the trunk was adjusted, but it didn't fix the problem. They ripped out the OEM XM receiver (under the back seat), replaced it and the cable to the head unit, and voila, everything works.
The tech tried to tell us that they'd never experienced that problem before, but then contradicted himself by saying that they knew the OEM XM manufacturer had sent out a huge batch of bad receivers and they'd just replaced one in a car the day previous!

Soooo....in case anyone else encounters this problem, and has the OEM XM receiver, you may want to point your service dept in this direction. This problem had been an ongoing one for me since December 10th.
On an unrelated note, in that two-and-a-half hours, the service department completely forgot that I was the owner of the car, and assured my father they'd mail HIM the paperwork, gave HIM a free oil change/tire rotation, and handed HIM the fob (yes, I was standing right there). Despite the fact I'd been in there at least six times in two months dealing with the same problem, and that I'm a 27-year-old woman, not some kid with their first car! Needless to say, after I get my free oil change, I'm taking my business to a different dealership!
I'm sorry some of the details are a little vague, but the techs were talking in circles and contradicting themselves until I was confused too. If anyone is interested in further details, let me know and I'll post the explanation from the paperwork when I get it (unless they mail it to my father first!)