Since it was successful I decided to make a new thread with an appropriate title. A pit bull bit my RX100 and shattered the LCD - no other damage obvious and it still took photos. Sony repair told me it would cost $300 to fix and it wasn't worth doing. So I ordered a replacement LCD from Amazon.http://www.amazon.com/gp/product/B00C5U ... UTF8&psc=1
The LCD (marked Sony, so I assume it's OEM) arrived without any instructions. It took a while to squeeze support out of the vendor. They sent me a PDF with exploded diagrams and instructions on how to open the camera, but it was not obvious how to remove the LCD itself. Further inquiry to the vendor got me a Youtube video in German for a different Sony camera LCD replacement. The step to remove the LCD was again, not obvious and for a different model.
Since there were no screws holding it in the back plate, I pushed gently and by golly the LCD came out. I still had to pry it off its adhesive backing, but the new LCD dropped into place fairly easily. I'm a bit worried that the PDF told me to replace this adhesive backing, but a new one did not come with the LCD. The really tricky part was inserting the flat electrical connector into the slot in the main body; the connector has a small bit of reinforcement to keep it from being a complete floppy connection, but it took a while to get it into the slot. (In fact, I closed the camera, turned it on and got no image the first try, so I tried again.)
So, for $90 I got a new LCD that is working. I am amazed that (1) I was able to do this and (2) unhappy that Sony repair was so reluctant and (3) disappointed that the vendor's "free technical support" was minimal. Still, all's well that ends well. I now have a unique RX100 - two pit bull tooth marks on the front.