I did as you suggested, converting to Twenty Eleven, and the mobile theme fo Twenty Eleven works on my iPhone5. Thank you. We're almost there!
It still does not offer me a way to revert to the mobile theme on my iPad 2, however. Rather than show a tiled first page or abbreviated postings, each post is displayed in full. There is still no "switch", at the end of the page, to go back-and-forth between theme display types as is indicated in the forum posts. The switch is present, however, on the end of the webpage when viewed on my iPhone.
Thank you for your help thus far.