Solved (at least partially). But first, I must rant: the custom partitioning screen is one of the most unintuitive I've ever seen!
I still don't know why I couldn't delete existing partitions and then add them back. Perhaps if I had done this in two steps it might have worked; i.e., deleting the partitions and selecting "Done", then going back to add new partitions. Anyway, I abandoned that approach.
What did work finally was in reconfiguring the existing partitions. The "Configure" icon below the partition list never did anything -- it stayed grayed out whatever I tried. By selecting the partition I wanted to re-use, I initially thought that all of the boxes to the right were grayed out. However, the "Reformat" and "Encrypt" boxes are not. If the existing partition is already formatted as Linux partition, other boxes are operational, but my partition had been zeroed out. Apparently anaconda is very finicky: you must check the "Reformat" box first, then specify the file system (ext4) second, and finally specify the mount point and Label.