One frustrating month later, I am submitting what I expect to be the closing article in this thread.

After several unsuccessful attempts to get 13.04 installed on my mdadm- and MBR-based RAID1 (how DID I manage to do it with 11.10, and with 12.04?), I took the hint from the 13.04 installer, which gently suggests using LVM. I disassembled my RAID (which was surprisingly difficult), and built an LVM configuration instead. I am now operating 13.04 on my system.

However, I am currently only using one of my two internal hard drives. I am operating without the automatic backup that the RAID1 provided me. That backup saved me days of hassle once, when one of my two drives failed. It is my understanding that LVM offers a mirroring feature. I have the second hard drive waiting. I am hoping to set up a fully-bootable mirror of my hard drive (that means mirroring every partition). This probably isn't the thread in which to pursue that discussion. So I guess I'll end things here, unless someone wants to chime in.