Winegard finally did call me back yesterday, but the results were less than I had hoped for. They told me that they had discontinued manufacture of my old fold-up dish several years ago, and no longer stocked replacement parts. They referred the call to tech service, and when they called me back, they confirmed that there was no comparable part from a later model.
There are fold-up dishes available from other manufacturers, but from what I could see online, I wasn't impressed, so I ended up ordering a tripod mounted dish like the one above. There were several listings for this one on EBay, and the price ranged all over the place - mostly in the $80 range, but as high as $100. I ordered the least expensive one at $59, and got a confirmation that it had shipped a few hours later.