I solved the problem. Sadly, however, the problem could have been solved two ways. I did a reinstall of Banshee, basically creating a new database. I had files coming from three different sources into the Banshee library and I only wanted one. After that was fix, I reloaded my Rockbox iPod and when I went to sync it with new material later, I waited until Banshee finished loading iPod device. Everything is copacetic now.
The next think I need to figure out is how to get my play count from Rockbox to Banshee, but that's another story.
What format are your tracks in? And when your iPod is connected and you
right-click on it in Banshee and click Properties, what is its "convert
tracks to this format" setting set to?
Banshee won't do a full sync if it recognises the tracks that are on
there already. It should recognise the tracks if they're the same as in
your library (i.e. they didn't get transcoded to another format).
You should be able to turn off the transcoding (I think it is one of the
options in the drop-down), but if Banshee thinks that the files are in a
format that your player doesn't support then it just won't load them
onto the player.