I've received a number of suggestions and explanations regarding the problem I've been having with my Panasonic DVD Recorder. One gent — and I'll thank him by name once I'm sure he's right — told me to switch from 4X disks to 1X. The Panasonic manual doesn't seem to say what kind to use (other than to recommend "Panasonic brand") and neither does their website. I started using 4X since that's what what my Pioneer DVD Recorder likes and for more than a month, they worked fine in the Panasonic, too.
Today, I went by CompUSA and bought a batch of 1X DVD blanks of their house brand, and also some 2X from TDK. So far, I've dubbed about three of each in the Panasonic with no problem. So things are definitely looking better. If I get through another dozen or so without a problem, I may declare the matter solved.