The good news is that I can return this part for part credit, and there are other Chevy Astros and GMC Safaris in their yard. Maybe we can find one that's older and has the correct mounting bracket to fit on my van. The bad news is that hiking around a junkyard in this heat is No Fun.
Lisa put the old bracket with the temporary fix back in place. It helps. I felt better when she told me that she would have made exactly the same mistake I did, because the mounts both look the same until you hold them right up against each other.