Just because I’m stubborn, I took a chance and tried again with the software update.  As before, the install froze up and failed.  This time, I managed to repeat the steps to get out, shut down, and power up, and fortunately I was able to get back in.  I’ve learned my lesson—they can keep their dysfunctional El Capitan 10.11.4!  I’m sure I can continue to manage without it.  I’m just happy to be able to post this.  If anyone out there is familiar with this glitch, please feel free to advise.