So, this is what I finally did:
- Checked off the "Sync Music" box
- All music removed from iPhone
- Re-checked the "Sync Music" box
- Clicked Apply/Sync
- Went to the "On This Phone" tab at the top
- As the greyed-out songs were syncing, I watched the entire process
- As soon as I noticed the "timer" start to go slow on the left side, I anticipated a potential issue
- A couple of times, the "timer" slowed completely and the sync timed out
- Went to the "Music" are and unchecked that entire artist from the sync
- Re-clicked Apply/Sync
- It processed completely
It seems the problem was that, for some reason, there are issues with these songs syncing now (not sure why), but it's causing the timeout of the sync, at least for the issue I was having. I'm going to go back and try to re-sync these artists/songs and see if it works now. But I'm too tired to do that now