Problem fixed - it was a problem on the server side that was causing the server for my host to send a Content-Type: text/plain.
I had added the string "AddType application/epub+zip .epub" to my .htaccess file, but it did not fix the problem. Using the Rex Swain's HTTP Viewer, I was able to compare the header for the file coming off of my site with the header for a file from a known working site (Gutenberg). I was still getting the Content-Type: text/plain. I found that there's a configuration parameter in the Apache httpd.conf file that has to be set to allow AddType to work. I called the hosting company and they made that change as well as some change to an encoding setting and it now appears to work.
Thanks everyone for your help in pointing me in the right direction.