After a stroke of luck, I found my problem and resolved it. I also resolved "waiting for changes," "Other" too large, and the Red-Ring-of-Death by my songs. I discovered that I and the problem and my wife did not because she has a 64-bit machine while I have a 32-bit machine. This is a problem because the 11.4 iTunes from Apple requires a 64-bit machine (it even says so in the bottom left portion of the screen: http://www.apple.com/itunes/download/). I had downloaded the 64-bit iTunes and had problems ever since. Here are all the steps I performed in a very specific order:
Calendar invitation problem -- clean install of iTunes:
1. Connect iPhone to iTunes,
2. If a sync starts, cancel it,
3. Transfer purchases,
4. Backup iPhone to computer,
5. Uncheck everything: apps, tones, music, movies,TV shows, podcasts, books, and photos,
6. Re-sync,
7. Backup again to computer,
8. Delete iOS updates:
a. C:\Users\Steve\AppData\Roaming\Apple Computer\iTunes\iPhone Software Updates\all files,
b. C:\Users\Steve\AppData\Roaming\Apple Computer\iTunes\iPad Software Updates\all files,
9. In Control Panel\Programs\Programs and Features, uninstall:
a. iTunes,
b. Apple Application Support,
c. Apple Mobile Device Support,
d. Apple Software Update,
e. Bonjour,
10. Unplug iPhone from computer,
11. Repair registry if you have the software; I use PC Tools Registry Mechanic, but others are available,
12. Reboot your computer,
13. Download 32-bit iTunes from http://filehippo.com/download_itunes_32
14. Install 32-bit iTunes,
15. From iTunes:
a. Now is the time if you want to reorganize your libraries, rename files, etc,
b. Populate iTunes with your libraries from File>Add Folder to Library,
c. When that is done, in your music library, right-click on any song and select Get Album Artwork,
d. When that is done, turn on and update Genius.
"Other" large problem and the Red-Ring-of-Death:
1. Re-connect your iPhone to iTunes
2. Restore iPhone from backup done in step 4.
3. If your "Other" is more that 2 GB, restore the backup from step 7.
4. Uncheck "Automatically sync when this iPhone is connected,"
5. Uncheck "Sync with this iPhone over Wi-Fi,"
6. On your iPhone, go to Settings>iTunes & App Store>iTunes Match>Off; this gets rid of the Red-Ring-of-Death by your music,
7. Backup iPhone to computer,
8. Your calendar should have all your invitations and the ability to send invites as well.
This last part keeps "Other" large from coming back. "Other" grows when syncs are interrupted. Sometimes it comes from corrupt Voice Memos, sometimes from corrupt music. To eliminate interrupted syncs, I now do my restores in many steps, not one big one. When my 6+ arrives, this is also how I will transfer all my information to my new phone.
Sync in the order of fewest files to most files without ever cancelling the sync:
1. Sync Tones,
2. When finished, sync Podcasts,
3. When finished, sync Books and Audiobooks,
4. When finished, sync Apps,
5. When finished, sync Photos,
6. Backup iPhone to computer,
7. When finished, sync Music:
a. For my machine, it takes about 7 seconds to add a song to my iPhone which rounds to about 500 songs an hour,
b. Plan your syncs in 1 hour increments so that you never risk needing to cancel a sync mid-stream,
8. Check "Automatically sync when this iPhone is connected,"
9. Check "Sync with this iPhone over Wi-Fi."
10. Backup iPhone to computer,
11. Backup iPhone to iCloud.
I have a 64GB phone running iOS 8.0.2 an iTunes 11.4.0.18 32-bit, 4 tones, 2 podcasts, 13 books, 1 audiobook, 156 Apps, 1203 Photos, and 9688 songs, and 2 GB "Other."
Good luck to you all.