Okay, so I went to the genius bar today and spoke to two Apple geniuses, each of whom had a possible solution. Neither one worked for me, but both are good ideas and they may work for someone reading this thread so I'll include them here. I also tried one other thing which worked for me. I'll list that below.
Genius 1's Idea - Do a complete uninstall of iTunes before reinstalling. SInce there is no uninstaller for iTunes, she suggested a program called AppZapper, which would remove iTunes and all associated files. I tried this and AppZapper works fast as advertised. Unfortunately, it fixed nothing.
Genius 2's Idea - He was convinced it was a system problem so he suggested a clean install of the operating system, which would require a backup of all files and downloaded apps. SInce I wasn't prepared to go to such extreme measures just yet, I tried one more thing which I should have tried much earlier...
My Idea - I launched Disk Utility and ran Verify Disk, followed by Repair Permissions. It found and repaired many damaged resource files, most of them belonging to iTunes, Image Capture, and iPhoto, the exact programs that were unable to see my iPhone. Anyway, this worked. iTunes kicks in instantly upon plugging in the iPhone, and appears in the Devices list just as it should. And it may be my imagination, but everything seems to run a little zippier now.
So Genius 2 was half right. It was the system that was broken. But doing a clean install turned out to be unnecessary.
Hope this helps.
