It looks like the latest Scruff beta might have been the culprit. The problem recurred after my reload, and knowing that was the only thing besides the Amazon App Store that I sideloaded, I uninstalled it. The problem hasn't happened afain, but there is still a bit more daylight left today.
Finally... we've gotten somewhere. It wasn't Scruff or Amazon App Store... it appears that my device is defective.
I was looking at an apartment today using the Xoom's camera to take pictures of some of the rooms. I started noticing some blue pixelation in the photos I was taking, and after about 5 photos, the media storage app crashed and the camera force-closed. The device was back in the state that I described where everything was force-closing, specifically apps that accessed my Google account. I rebooted my Xoom and resorted to using my Droid to take pics. When I got home, I noticed that my Xoom was still rebooting, so forced a hard reboot and, again, noticed the pixelation in the camera as well as some trailing that came out in my pics. After another minute or two, the apps started force-closing. I decided that it was time for a trip to the Verizon store.
Here's where the story gets a little more disappointing. I expected that since I purchased my Xoom on 2/28 (less than 30 days ago), I could just swap it out. However, since Verizon changed their return policy to 14 days, I have to go through the warranty... which means Motorola is shipping me a box to send back my Xoom within 2 business days and I'll receive it back either repaired or replaced (or possibly determined to be not faulty? hopefully not!) within 3 business days.
I did go through some "troubleshooting" over the phone, which involved checking some unrelated settings. The guy was in good humor about it -- recognizing from the way I described the problem that I was a savvy user and sparing me the painful step-by-step instruction of each setting. We even went through a factory reset and the camera issue persisted, and after a short period of time, the force close came back. And after another few minutes it just spontaneously went into a reboot loop.
So... to make a long story ... a little less long? It looks like something is defective with my Xoom. I'm disappointed that I pretty much can't use it now... I have to wait to get the box... and then I'll be without it for nearly a week. I just hope all of this has happened early on enough that I won't get stuck with a refurb if they determine that mine needs to be replaced.